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

MIT 18.01 Single Variable Calculus (OCW)
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\[\lim_{x\to \frac{\pi}{2}} \frac{\sin x}{x}\] 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?
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.
1/(pi/2) = 2/pi

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