Question

Evaluate
\[\lim_{x \rightarrow 1} \frac{cos(\frac{\pi x}{2})}{1-x}\]

Answer 1

l'hospital allowed?

Answer 2

Not allowed..

Answer 3

rats

Answer 4

substitute let y=x-1

Answer 5

* y=1-x

Answer 6

\[\lim_{y\to0}\frac{\cos(\frac\pi2(y+1))}{y}\]???

Answer 7

changes to -sin
okay I see it now :)

Answer 8

\[\lim_{x \rightarrow 1} \frac{cos(\frac{\pi x}{2})}{1-x}\]\[=\lim_{y \rightarrow 0} \frac{cos(\frac{\pi (1-y)}{2})}{y}\]\[=\lim_{y \rightarrow 0} \frac{cos(\frac{\pi }{2}-\frac{\pi y}{2})}{y}\]\[=\lim_{y \rightarrow 0} \frac{sin(\frac{\pi y}{2})}{y}\]\[=\frac{\pi}{2}\]?

Answer 9

oh yeah +sin

Answer 10

seems correct!!
http://www.wolframalpha.com/input/?i= \lim_{x+\rightarrow+1}+\frac{cos%28\frac{\pi+x}{2}%29}{1-x}

Answer 11

Yeah!~ Thanks!!~