Question

how do i find the limit as x approaches pi/2 of (sinx/x)

Answer 1

\[\lim_{x\to \frac{\pi}{2}} \frac{\sin x}{x}\]

What is the value that sin(x) assumes when x approaches pi/2 ?
What is the value that x assumes when x approaches pi/2? (trivial)

The limit of a ratio is the ratio of the limits
\[\lim_{x \to \frac{\pi}{2}} \frac{\sin x}{x} = \frac{\lim_{x \to \frac{\pi}{2}} \sin x}{\lim_{x \to \frac{\pi}{2}} x}\]

Can you complete the exercise?

Answer 2

That function is continuous everywhere except at x=0. That means this limit is calculated by plugging pi/2 into the function to get the answer directly.

Answer 3

1/(pi/2) = 2/pi