Texas Instruments TI-89 User Manual - Page 845

nCr( ) MATH/Probability menu nCr(expression1, expression2) ⇒ expression For integer expression1 and expression2 with expression1 , expression2 , 0, nCr() is the number of combinations of expression1 things taken expression2 at a time. (This is also known as a binomial coefficient.) Both arguments can be integers or symbolic expressions. nCr(expression, 0) ⇒ 1 nCr(expression, negInteger) ⇒ 0 nCr(z,3) ans(1)|z=5 nCr(z,c) ans(1)/nPr(z,c) zø (zì 2)ø (zì 1) 6 10 z! c!(zì c)! 1 c! nCr(expression, posInteger) ⇒ expressionø (expressionì 1)... (expressionì posInteger+1)/ posInteger! nCr(expression, nonInteger) ⇒ expression!/ ((expressionì nonInteger)!ø nonInteger!) nCr(list1, list2) ⇒ list Returns a list of combinations based on the corresponding element pairs in the two lists. The arguments must be the same size list. nCr({5,4,3},{2,4,2}) ¸ {10 1 3} nCr(matrix1, matrix2) ⇒ matrix Returns a matrix of combinations based on the corresponding element pairs in the two matrices. The arguments must be the same size matrix. nCr([6,5;4,3],[2,2;2,2]) ¸ [165 130] nDeriv( ) MATH/Calculus menu nDeriv(expression1, var[, h]) ⇒ expression nDeriv(expression1, var, list) ⇒ list nDeriv(list, var[, h]) ⇒ list nDeriv(matrix, var[, h]) ⇒ matrix Returns the numerical derivative as an expression. Uses the central difference quotient formula. h is the step value. If h is omitted, it defaults to 0.001. When using list or matrix, the operation gets mapped across the values in the list or across the matrix elements. Note: See also avgRC() and d(). nDeriv(cos(x),x,h) ¸ limit(nDeriv(cos(x),x,h),h,0) ¸ ë sin(x) nDeriv(x^3,x,0.01) ¸ 3.ø (xñ +.000033) nDeriv(cos(x),x)|x=p/2 ¸ ë 1. nDeriv(x^2,x,{.01,.1}) ¸ {2.øx 2.øx} NewData CATALOG NewData dataVar, list1[, list2] [, list3]... Creates data variable dataVar, where the columns are the lists in order. Must have at least one list. list1, list2, ..., listn can be lists as shown, expressions that resolve to lists, or list variable names. NewData makes the new variable current in the Data/Matrix Editor. NewData mydata,{1,2,3},{4,5,6} ¸ Done (Go to the Data/Matrix Editor and open the var mydata to display the data variable below.) NewData dataVar, matrix Creates data variable dataVar based on matrix. Appendix A: Functions and Instructions 845