question 9

We want to compute the following limit lim sin(2(x - 1)) z-41 sin(x - 1) a) As z approaches 1 we get an indeterminate form of the type 0/0 00/00 00- 00 0 00 0 0 x 00 0 100 b) We want to simplify the quotient sin(2(z-1)) sin(z-1) for z # 1, so that it no longer gives an indeterminate form at a = 1. HINT: Use trigonometric identities. Answer : c) Use your result in (b) to compute lim sin (2(2 - 1)) 241 sin(2 - 1)