# Texas Instruments TI-36X Pro User Manual

## Texas Instruments TI-36X Pro Manual

### Texas Instruments TI-36X Pro manual table of contents:

- Texas Instruments TI-36X Pro | User Manual - Page 1

TI-36X Pro Calculator Important information...2 Examples ...3 Switching the calculator on and off ...3 Display contrast ...3 Home screen ...3 2nd ... Order of operations...11 Clearing and correcting...13 Fractions...13 Percentages...15 EE key ...16 Powers, roots and inverses ...17 Pi...18 Math...19 ... - Texas Instruments TI-36X Pro | User Manual - Page 2

... information...76 In case of difficulty ...77 Texas Instruments Support and Service...78 Important information Texas ... exclusive liability of Texas Instruments, regardless of the form of action, shall not exceed the purchase price of this product. Moreover, Texas Instruments shall not be liable for ... - Texas Instruments TI-36X Pro | User Manual - Page 3

Examples Each section is followed by instructions for keystroke examples that demonstrate the TI-36X Pro functions. Examples assume all default settings, as... other instructions. The answers are displayed on the Home screen. The TI-36X Pro screen can display a maximum of four ... - Texas Instruments TI-36X Pro | User Manual - Page 4

... 2ND FIX SCI, ENG DEG, RAD, GRAD L1, L2, L3 H, B, O Definition 2nd function. Fixed-decimal setting. (See Mode section.) Scientific or engineering notation. (See Mode section.) Angle mode (degrees, radians, or gradians). (See Mode section.) Displays ... - Texas Instruments TI-36X Pro | User Manual - Page 5

... is displayed above it. Press % to activate the secondary function of a given key. Notice that 2ND appears as... data, press % again. For example, % b 25 < calculates the square root of 25 and returns ... remain maximal. NORM displays results with digits to the left and right of the decimal, as in 123456.... - Texas Instruments TI-36X Pro | User Manual - Page 6

... from 1 to 999 times 10 to an integer power. The integer power is always a multiple of 3. Note: E is a shortcut key to enter a number in scientific notation format. The result displays in the numeric notation format selected in the mode menu. FLOAT 0 1 2... - Texas Instruments TI-36X Pro | User Manual - Page 7

Examples of Classic and MathPrint™ modes Classic mode Sci MathPrint™ mode Sci Float mode and answer toggle key. Float mode and answer toggle key. Fix 2 Fix 2 and answer toggle key. U n/d U n/d Exponent example Exponent example Square root example Square root example Cube root example... - Texas Instruments TI-36X Pro | User Manual - Page 8

... keys A multi-tap key is one that cycles through multiple functions when you press it. For example, the X key contains the trigonometry functions sin ... of this guidebook describe how to use the keys. Menus Menus give you access to a large number of calculator functions. Some menu keys, such as % h, ... - Texas Instruments TI-36X Pro | User Manual - Page 9

d (key with multiple menus): MATH 1:4n/d³´Un/d 2: lcm( 3: gcd( 4: 4Pfactor 5: sum( 6: prod( NUM 1: abs( 2: round( 3: iPart( 4: fPart( 5: int( 6: min( 7: max( 8: mod( DMS 1: ¡ 2: ¢ 3: £ 4: r 5: g 6: ´DMS R ³´ P 1: P ´Rx( 2: P ´Ry( 3: R ´Pr( 4: R ´Pq( Scrolling expressions and history ... - Texas Instruments TI-36X Pro | User Manual - Page 10

... %b8< r Last answer %i The last entry performed on the home screen is stored to the variable ans. This variable is retained in memory, even after the calculator is turned off. To recall the value of ans: • Press % i (ans displays on the screen), or • Press any operations key (T, U, and so ... - Texas Instruments TI-36X Pro | User Manual - Page 11

3%c%i < Order of operations The TI-36X Pro calculator uses Equation Operating System (EOS™) to evaluate expressions. Within a priority level, EOS evaluates functions from left to right and in the following order. 1st 2nd 3rd 4th 5th Expressions inside ... - Texas Instruments TI-36X Pro | User Manual - Page 12

... (nCr). Multiplication, implied multiplication, division. Addition and subtraction. Conversions (n/d³´Un/d, F³´D, 4DMS). < completes all operations and closes all open parentheses. Examples +QPM 6 0 T 5 V M1 2 < ( M) 1TM8T12< % b 9 T 16 < () 4V(2T3)< 4(2T3)< ^ and ‡ %b3G2"T4 G2< 12 - Texas Instruments TI-36X Pro | User Manual - Page 13

.... Clears variables x, y, z, t, a, b, c, and d to their default value of 0. Resets the calculator. Returns unit to default settings; clears memory variables, ...To compute more complex expressions (functions, variables, complex numbers, etc.), use W along with ( and ). The calculator defaults output to ... - Texas Instruments TI-36X Pro | User Manual - Page 14

• P enters a simple fraction. Pressing P before or after a number can result in different behavior. Entering a number before pressing P makes that number the numerator. To enter fractions with operators or radicals, press P before you enter a number (in MathPrint™ mode only). • In MathPrintମ. - Texas Instruments TI-36X Pro | User Manual - Page 15

... n/ n d ³´U /d F³´D 4%@1$2" %˜< Examples P1.2 T 1.3 $ 4 < (MathPrint™ mode only) (MathPrint™ P M 5 T % b 5 mode only) F U 4 ( 1 ) ( 6 )$2(1)< Percentages %_ To perform a calculation involving a percentage, press % _ after entering the value of the percentage. Example 2 % _ V 150 < 15 - Texas Instruments TI-36X Pro | User Manual - Page 16

... _ V 7300 < V 280 < The two extractions represent a total of 317.9 tons of metal for a total value of 89012 dollars. EE key E E is a shortcut key to enter a number in scientific notation format. Example 2E5< q$"< -< 16 - Texas Instruments TI-36X Pro | User Manual - Page 17

Powers, roots and inverses F Calculates the square of a value. The TI-36X Pro calculator evaluates expressions entered with F and a from left to right in both Classic and MathPrint™ modes. Raises a value to the power indicated. Use " ... - Texas Instruments TI-36X Pro | User Manual - Page 18

2%a< Pi g (multi-tap key) p = 3.141592653590 for calculations. p = 3.141592654 for display. Example p 2Vg< r ³ Problem What is the area of a circle if the radius is 12 cm? Reminder: A = p×r2 g V 12 F < r The area of the circle is 144... - Texas Instruments TI-36X Pro | User Manual - Page 19

Math d MATH d displays the MATH menu: 1:4n/d³´Un/d 2: lcm( 3: gcd( 4: 4Pfactor 5: sum( 6: prod( Examples n/ n d³´U /d Converts between simple fractions and mixed-number form. Least common multiple Greatest common divisor Prime factors Summation Product 9P2"d1< lcm( d2 6%`9)< d3 18 % ` 33 ) ... - Texas Instruments TI-36X Pro | User Manual - Page 20

Number functions d NUM d " displays the NUM menu: 1: abs( 2: round( 3: iPart( 4: fPart( 5: int( 6: min( 7: max( 8: mod( Examples abs( d"1 M%b5< d"2 1.245 % ` 1 5 < 4.9 L z < d "3 z ) < d "4 z ) V3< d "5 M 5.6 ) < d "6 4 % `M5 ) < d "7 .6 % ` .7 ) < Absolute value Rounded value Integer part of a ... - Texas Instruments TI-36X Pro | User Manual - Page 21

mod( d "8 17 % ` 12 6 < Angles d DMS d " " displays the DMS menu: 1: ¡ 2: ¢ 3: £ 4: r 5: g 6: ´DMS Specifies the angle unit modifier as degrees (º). Specifies the angle unit modifier as minutes ('). Specifies the angle unit modifier as seconds ("). Specifies a radian angle. Specifies a ... - Texas Instruments TI-36X Pro | User Manual - Page 22

DEG q< 2gd""4 < 4DMSS 1.5 d " " 6 < ³ Problem Two adjacent angles measure 12¡ 31¢ 45£ and 26... 39 degrees, 26 minutes and 23 seconds. ³ Problem It is known that 30¡ = p / 6 radians. In the default mode, degrees, find the sine of 30¡. Then set the calculator to radian mode and calculate the ... - Texas Instruments TI-36X Pro | User Manual - Page 23

Note: Press - to clear the screen between problems. - X 30 ) < q" - Texas Instruments TI-36X Pro | User Manual - Page 24

...4) gives (r, q) = (5.0, 53.1). Trigonometry X Y Z (multi-tap keys) Enter trigonometric functions (sin, cos, tan, sin-1, cos-1, tan-1), just as you would write them. Set the desired Angle mode before starting trigonometric calculations. Example Degree Mode tan q$$ - Texas Instruments TI-36X Pro | User Manual - Page 25

tan-1 Z Z1 ) < r cos 5VYgP4") < r ³ Problem Find angle A of the right triangle below. Then calculate angle B and the length of the hypotenuse c. Lengths are in meters. Round results to one decimal place. Reminder: 7 7⎞ - therefore m±A = tan-1 ⎛ -tan A = -⎝ 3 - Texas Instruments TI-36X Pro | User Manual - Page 26

... multi-tap keys repeatedly lets you access the corresponding hyperbolic or inverse hyperbolic function. Angle modes do not affect hyperbolic calculations. Example Set floating q $ $ < decimal HYP XXX5)T2 < ## - Texas Instruments TI-36X Pro | User Manual - Page 27

...you specify. Examples LOG D D1 ) < LN D5)V2< 10 › C CD D 2)< D DC C 5")< C .5 < e› Numeric derivative %A % ...derivative of expression with respect to variable, given the value at which to calculate the derivative and H (if not specified, the default is 1EM3). This function is valid only for ... - Texas Instruments TI-36X Pro | User Manual - Page 28

...investigations. You can use nDeriv( once in expression. Because of the method used to calculate nDeriv(, the calculator can return a false derivative value at a nondifferentiable point. ³ Problem Find the slope of the tangent line to the curve ... - Texas Instruments TI-36X Pro | User Manual - Page 29

... the function must be at this point! Numeric integral %Q % Q calculates the numeric function integral of an expression with respect to a variable x, given...RAD angle mode % Q q " - Texas Instruments TI-36X Pro | User Manual - Page 30

< Notice that both areas are equal. Since this is a parabola with the vertex at (4,0) and zeros at (M2, 0) and (2, 0) you see that the symmetric areas are equal. Stored operations %m %n % n lets you store a sequence of operations. % m plays back the operation. To set an operation and then recall ... - Texas Instruments TI-36X Pro | User Manual - Page 31

...y = 5x - 2, calculate y for the following values of x: -5; -1. %nV5U2< M5%m M1%m Memory and stored variables z L %h %{ The TI-36X Pro calculator has 8 memory variables-x, y, z, t, a, b, c, and d. You can store a real or complex number or an expression result to a... - Texas Instruments TI-36X Pro | User Manual - Page 32

z is a multi-tap key that cycles through the variable names x, y, z, t, a, b, c, and d. You can also use z to recall the stored values for these variables. The name of the variable is inserted into the current entry, but the value assigned to the variable is used to evaluate the expression. To ... - Texas Instruments TI-36X Pro | User Manual - Page 33

Lzz < zz - Texas Instruments TI-36X Pro | User Manual - Page 34

... list can contain up to 42 items. Press % # to go to the top of a list, and % $ to go to the bottom of a list. List formulas accept all calculator functions and real numbers. Numeric notation, decimal notation, and angle modes affect the display of an element (... - Texas Instruments TI-36X Pro | User Manual - Page 35

< v - Texas Instruments TI-36X Pro | User Manual - Page 36

... menu of statistical result variables. Use $ and # to locate the desired variable, and press < to select it. If you select this option before calculating 1-Var stats, 2-Var stats, or any of the regressions, a reminder appears. Analyzes statistical data from 1 data set with 1 measured variable, x. ... - Texas Instruments TI-36X Pro | User Manual - Page 37

3: 2-Var Stats 4: LinReg ax+b 5: QuadraticReg 6: CubicReg 7: LnReg a+blnx 8: PwrReg ax^b 9: ExpReg ab^x Analyzes paired data from 2 data sets with 2 measured variables-x, the independent variable, and y, the dependent variable. Frequency data may be included. Note: 2-Var Stats also computes ... - Texas Instruments TI-36X Pro | User Manual - Page 38

...following distribution functions: 1: Normalpdf Computes the probability density function (pdf) for the normal distribution at a specified x value. The defaults are mean ...specified by mean mu and standard deviation sigma. It calculates the x value associated with an area to the left of the x value. 0 ... - Texas Instruments TI-36X Pro | User Manual - Page 39

... stored in the StatVars menu until the next statistics or regression calculation. The results must be interpreted based on which type of statistics or ... help you interpret correctly, the title bar reminds you of which calculation was last performed. Variables n v or w Sx or Sy Definition Number of x ... - Texas Instruments TI-36X Pro | User Manual - Page 40

... Linear regression slope. Linear regression y-intercept. Correlation coefficient. Uses a and b to calculate predicted x value when you input a y value. Uses a and b to calculate predicted y value when you input an x value. Minimum of x values. Median of the elements between MinX ... - Texas Instruments TI-36X Pro | User Manual - Page 41

1-Var Example Find the mean of {45, 55, 55, 55} Clear all data Data vv$$$ < 45 $ 55 $ 55 $ 55 < %s %u 2 (Selects 1-Var Stats) $$ < Stat Stat Var 2< V2< 2-Var Example Data: (45,30); (55,25). Find: x¢(45) Clear all data Data vv$$$ < 45 $ 55 $ " 30 $ 25 $ 41 - Texas Instruments TI-36X Pro | User Manual - Page 42

... grade (weighted average). 2. What does the value of n given by the calculator represent? What does the value of Gx given by the calculator represent? Reminder: The weighed average is Σx ( 12 ) ( 1 ) + ( 13 ) ( 0.5 ) + ( 10 ) ( 1 ) + ( 11 ) ( 0.5 n 1 + 0.5 + 1 + 0.5 3. The teacher gave ... - Texas Instruments TI-36X Pro | User Manual - Page 43

... $ " 1 $ .5 $ 1 $ .5 < %u 2 (Selects 1-Var Stats) $""< < Anthony has an average (v) of 11.33 (to the nearest hundredth). On the calculator, n represents the total sum of the weights. n = 1 + 0.5 + 1 + 0.5. Gx represents the weighted sum of his scores. (12)(1) + (13)(0.5) + (10)(1) + (11)(0.5) = 34... - Texas Instruments TI-36X Pro | User Manual - Page 44

³ Problem The table below gives the results of a braking test. Test No. Speed (kph) Braking distance (m) 1 33 5.30 2 49 14.... 55 kph. A hand-drawn scatter plot of these data points suggest a linear relationship. The calculator uses the least squares method to find the line of best fit, y'=ax'+b, for ... - Texas Instruments TI-36X Pro | User Manual - Page 45

... of 18.59 meters for a vehicle traveling at 55 kph. Regression example 1 Calculate an ax+b linear regression for the following data: {1,2,3,4,5}; {5,8,11,14,17}. ... $$$$ < Press $ to examine all the result variables. Regression example 2 Calculate the exponential regression for the following data: 45 - Texas Instruments TI-36X Pro | User Manual - Page 46

... equation to f(x) in the I menu. Regression Equation Find the average value (y) of the data in L2 using StatVars. < %u 1 (Selects StatVars Notice that the title bar reminds you of your last statistical or regression calculation. Examine the I 2 table of values of the regression equation. 46 - Texas Instruments TI-36X Pro | User Manual - Page 47

... 2-Var Stats on your data, the variables a and b (along with r and r2) will be calculated as a linear regression. Do not recalculate 2-Var Stats after any other regression calculation if you want to preserve your regression coefficients (a, b, c, d) and r ... - Texas Instruments TI-36X Pro | User Manual - Page 48

< Probability H % - Texas Instruments TI-36X Pro | User Manual - Page 49

nPr 8HHH3< STO 4 rand 5L% - Texas Instruments TI-36X Pro | User Manual - Page 50

...set up a function table: 1. Press I and select Edit function. 2. Enter a function and press - Texas Instruments TI-36X Pro | User Manual - Page 51

...points closer to (18, 324). ³ Problem A charity collected $3,600 to help support a local food ... run out. How many months will the charity support the kitchen? Reminder: If x = months and ... z < 0 $ 1 $" < $ < Input each guess and press - Texas Instruments TI-36X Pro | User Manual - Page 52

... % t displays the matrix NAMES menu, which shows the dimensions of the matrices and lets you use them in calculations. 1: [A] 2: [B] 3: [C] 4: [Ans] 5: [I2] 6: [I3] Definable matrix A Definable matrix B Definable matrix C Last matrix result (... - Texas Instruments TI-36X Pro | User Manual - Page 53

Matrix example Define matrix [A] as 1 2 3 4 Calculate the determinant, transpose, inverse, and rref of [A]. Define [A] % t ! < Set " - Texas Instruments TI-36X Pro | User Manual - Page 54

... ...NAMES % ...displays the vector NAMES menu, which shows the dimensions of the vectors and lets you use them in calculations. 1: [u] 2: [v] 3: [w] 4: [Ans] Definable vector u Definable vector v Definable vector w Last matrix result (displayed as [Ans]=m×n) or last ... - Texas Instruments TI-36X Pro | User Manual - Page 55

...MATH menu, which lets you perform the following vector calculations: 1: DotProduct 2: CrossProduct 3: norm magnitude Syntax:...[w]. Vector example Define vector [u] = [ 0.5 8 ]. Define vector [v] = [ 2 3 ]. Calculate [u] + [v], DotP([u],[v]), and norm([v]). Define [u] % ...! < " - Texas Instruments TI-36X Pro | User Manual - Page 56

Add vectors %...< T %...$< < DotP 5 V 2 T 8 V 3 < Note: DotP is calculated here in two ways. norm r< % b 2 F T 3 F" r< Note: norm is calculated here in two ways. Solvers Numeric equation solver %‰ % ‰ prompts you for the equation and the ... - Texas Instruments TI-36X Pro | User Manual - Page 57

Example Reminder: If you have already defined variables, the solver will assume those values. Num-solv %‰ Left side 1 P2 " zF U5 z z z z z "" Right side 6 z U z z zz z z < Variable values 1P2$ 2P3$ 0.25 $ "" Solve for b < Note: Left-Right is the difference between the left- and right-hand ... - Texas Instruments TI-36X Pro | User Manual - Page 58

Example of quadratic equation Reminder: If you have already defined variables, the solver will assume those values. Poly-solv % - Texas Instruments TI-36X Pro | User Manual - Page 59

System of linear equations solver %‹ % ‹ solves systems of linear equations. You choose from 2×2 or 3×3 systems. Notes: • x, y, and z results are automatically stored in the x, y, and z variables. • Use r to toggle the results (x, y and z) as needed. • The 2x2 equation solver solves for... - Texas Instruments TI-36X Pro | User Manual - Page 60

Toggle r result type Example 3×3 system Solve: 5x - 2y + 3z = -9 4x + 3y + 5z = 4 2x + 4y - 2z = 14 System solve 3×3 system First equation Second equation Third equation Solutions %‹$ < 5< M2 < 3< M9< 4< 3< 5< 4< 2< 4< M2 < 14 < < $ $ 60 - Texas Instruments TI-36X Pro | User Manual - Page 61

... 1: ´Hex 2: ´Bin 3: ´Dec 4: ´Oct Converts to hexadecimal (base 16). Converts to binary (base 2). Converts to decimal (base 10). Converts ... TYPE menu, which lets you designate the base of a number regardless of the calculator's current number-base mode. 1: h 2: b Designates a hexadecimal integer. ... - Texas Instruments TI-36X Pro | User Manual - Page 62

3: d 4: o Specifies a decimal number. Specifies an octal integer. Examples in DEC mode Note: Mode can be set to DEC, BIN, OCT, or HEX. See the Mode section. d ´Hex 127 % - 1 1 %-2< 10000000 % - " 2 %-4< #< h ´Bin b ´Oct o ´Dec Boolean logic % - ! displays the LOGIC menu, which lets you ... - Texas Instruments TI-36X Pro | User Manual - Page 63

...7 48 < Expression evaluation %‡ Press %‡ to input and calculate an expression using numbers, functions, and variables/parameters. Pressing %‡ from a populated home screen expression pastes the content to Expr=. If the user is in an input or output history line when %‡ is pressed, the home ... - Texas Instruments TI-36X Pro | User Manual - Page 64

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Note: Displayed constant values are rounded. The values used for calculations are given in the following table. Constant speed of light c g gravitational acceleration h Planck's constant NA Avogadro's number Value used for calculations 299792458 meters per second 9.80665 meters per second2 R me mp ... - Texas Instruments TI-36X Pro | User Manual - Page 66

Conversions The CONVERSIONS menu permits you to perform a total of 20 conversions (or 40 if converting both ways). To access the CONVERSIONS menu, press % -. Press one of the numbers (1-5) to select, or press # and $ to scroll through and select one of the CONVERSIONS submenus. The submenus include... - Texas Instruments TI-36X Pro | User Manual - Page 67

lb 4 kg kg 4 lb pounds to kilograms kilograms to pounds Temperature conversion Conversion ¡F 4 ¡C ¡C 4 ¡F ¡C 4 ¡K ¡K 4 ¡C Farenheit to Celsius Celsius to Farenheit Celsius to Kelvin Kelvin to Celsius Speed and length conversion Conversion km/hr 4 m/s m/s 4 km/hr LtYr 4 m m 4 LtYr pc 4 m... - Texas Instruments TI-36X Pro | User Manual - Page 68

Pressure conversion Conversion atm 4 kPa Pa 4 atm mmHg 4 kPa Pa 4 mmHg Examples Temperature (M22) atmospheres to Pascals Pascals to atmospheres millimeters of mercury to Pascals Pascals to millimeters of mercury %-2 - Texas Instruments TI-36X Pro | User Manual - Page 69

... %ˆ The calculator performs the following complex number calculations Addition, subtraction, multiplication, and division Argument and absolute ... Conjugate number calculations Setting the complex format: Set the calculator to DEC mode when computing with complex numbers. q $ $ $ Selects the REAL ... - Texas Instruments TI-36X Pro | User Manual - Page 70

Complex menu Description 1:± ± (polar angle character) Lets you paste the polar representation of a complex number (such as 5±p). 2 :polar angle angle( Returns the polar angle of a complex number. 3: magnitude abs( (or |þ| in MathPrint™ mode) Returns the magnitude (modulus) of a complex ... - Texas Instruments TI-36X Pro | User Manual - Page 71

... a+bi Conjugate: conj( % ˆ6 5 U 6 ggg ) < Real: real( % ˆ7 5 U 6 ggg) < Errors When the calculator detects an error, it returns an error message with the type ...invalid value for area invNormal. ARGUMENT - This error is returned if: • a function does not have the correct number of arguments. •... - Texas Instruments TI-36X Pro | User Manual - Page 72

... error. DATA TYPE - You entered a value or variable that is the wrong data type. • For a function (including implied multiplication) or an instruction, you entered an argument that is an invalid data type, such as a complex number where a real number is ... - Texas Instruments TI-36X Pro | User Manual - Page 73

... coefficient cannot be zero - This error is displayed if a in a Polynomial solver calculation is prepopulated with zero, or if the you set a to zero and ...and n in the DISTR menus. INVALID EQUATION - This error is returned when: • The calculation contains too many pending operations (more than 23). ... - Texas Instruments TI-36X Pro | User Manual - Page 74

...entered a type that is not allowed, such as a complex number, matrix, or vector, as an element in the stat list editor, matrix ... This error is displayed when: • A singular matrix (determinant = 0) is not valid as the argument for -1. • The SinReg instruction or a polynomial regression generated a... - Texas Instruments TI-36X Pro | User Manual - Page 75

... 1-var or 2-var stats with no defined data points, or attempted to calculate 2-var stats when the data lists are not of equal length. SYNTAX -... COMPLEX - If you use too many levels of MathPrint™ complexity in a calculation, the TOO COMPLEX error is displayed (this error is not referring to complex ... - Texas Instruments TI-36X Pro | User Manual - Page 76

...or explode, releasing hazardous chemicals. Discard used batteries according to local regulations. How to remove or replace the battery The TI-36X Pro calculator uses one 3 volt CR2032 lithium battery. Remove the protective cover and turn the calculator face... - Texas Instruments TI-36X Pro | User Manual - Page 77

... apply. See www.dtsc.ca.gov/hazardouswaste/perchlorate In case of difficulty Review instructions to be certain calculations were performed properly. Check the battery to ensure that it is fresh and properly installed. Change the battery when:... - Texas Instruments TI-36X Pro | User Manual - Page 78

Texas Instruments Support and Service For general information Home Page: education.ti....Islands: Always contact Texas Instruments Customer Support before returning a product for service. All ...leaflet enclosed with this product (hardware) or contact your local Texas Instruments retailer/distributor. 78

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