Texas Instruments voyage 200 User Manual - Page 831

limit( ) MATH/Calculus menu limit(expression1, var, point[, direction]) ⇒ expression limit(list1, var, point[, direction]) ⇒ list limit(matrix1, var, point[, direction]) ⇒ matrix Returns the limit requested. direction: negative=from left, positive=from right, otherwise=both. (If omitted, direction defaults to both.) limit(2x+3,x,5) ¸ 13 limit(1/x,x,0,1) ¸ ˆ limit(sin(x)/x,x,0) ¸ 1 limit((sin(x+h)-sin(x))/h,h,0) ¸ cos(x) limit((1+1/n)^n,n,ˆ) ¸ e Limits at positive ˆ and at negative ˆ are always converted to one-sided limits from the finite side. Depending on the circumstances, limit() returns itself or undef when it cannot determine a unique limit. This does not necessarily mean that a unique limit does not exist. undef means that the result is either an unknown number with finite or infinite magnitude, or it is the entire set of such numbers. limit() uses methods such as L'Hopital's rule, so there are unique limits that it cannot determine. If expression1 contains undefined variables other than var, you might have to constrain them to obtain a more concise result. Limits can be very sensitive to rounding error. When possible, avoid the APPROX setting of the Exact/Approx mode and approximate numbers when computing limits. Otherwise, limits that should be zero or have infinite magnitude probably will not, and limits that should have finite non-zero magnitude might not. limit(a^x,x,ˆ) ¸ limit(a^x,x,ˆ)|a>1 ¸ limit(a^x,x,ˆ)|a>0 and a