What is the limit as x approaches pi/2 of sin(1/x) ?

The limit as x approaches pi/2 of sin(1/x) is sin(2/pi)

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limit as x approaches pi/2 of sin(1/x)

x \to \frac{π}{2} lim (sin (\frac{1}{x}))

sin (\frac{2}{π})

Solution steps

x \to \frac{π}{2} lim (sin (\frac{1}{x}))

Plug in the value

x = \frac{π}{2}

= sin (\frac{1}{\frac{π}{2}})

Simplify

= sin (\frac{2}{π})

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What is the limit as x approaches pi/2 of sin(1/x) ?
The limit as x approaches pi/2 of sin(1/x) is sin(2/pi)