Use series to evaluate lim e x0 -(1+x) 2x X-0 2x (Type a simplified fraction.)
Use Taylor polynomials to evaluate the limit. e-3x – 1 7) lim X0 х sin 2x - sin 4x 8) lim x>0 х
7. Evaluate each of the following limits. tan x e-4x -e 4x a) lim x0 2x b) lim XOCOS X+1
Evaluate the following limit. Use l'Hôpital's Rule when it is convenient and applicable. lim x?cotx X0 lim x?cotx = x+0 (Type an exact answer.)
- 3e - sin(-5x) Find lim - 2x (x,y)+(0,0) -3e - sin(-5x) lim - 2x (x,y)-(0,0) (Type an integer or a simplified fraction.)
Use MacLaurin series to evaluate the following limits. Do not use L'Hospital's rule. (a) lim, 0 2x+cos 2-3 sino 1+36x3-1 (b) lim;-+0 sin(60)(et-1-2)
Evaluate the given definite integral. S (1-x)?dx dx = (Type an integer or a simplified fraction.)
sin Use the relation lim 00 = 1 to determine the limit of the given function. tan (4x) f(x) = х tan (4) lim x0 Х (Type an integer or a simplified fraction.)
Use the given Maclaurin series to evaluate the limit. x - ln (1 + x) lim x-0 ex - 1 - x
Evaluate the following limit using Taylor series. -X- In (1 - x) lim x→0 106² - x - In (1 – X) lim (Simplify your answer.) x→0 1082
(4) Use MacLaurin series to evaluate the following limits. Do not use L'Hospital's rule. (a) lim-0 21+ucos g -3 sin e 136.23-1 (b) lim 0 sin(6x)(e-1-1)