What is the limit as x approaches pi/4 of (4x)/(tan(x)) ?

The limit as x approaches pi/4 of (4x)/(tan(x)) is pi

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limit as x approaches pi/4 of (4x)/(tan(x))

x \to \frac{π}{4} lim (\frac{4 x}{tan ( x )})

π

Decimal

3.14159 \dots

Solution steps

x \to \frac{π}{4} lim (\frac{4 x}{tan ( x )})

Plug in the value

x = \frac{π}{4}

= \frac{4 \cdot \frac{π}{4}}{tan ( \frac{π}{4} )}

Simplify

\frac{4 \cdot \frac{π}{4}}{tan ( \frac{π}{4} )} : π

= π

What is the limit as x approaches pi/4 of (4x)/(tan(x)) ?
The limit as x approaches pi/4 of (4x)/(tan(x)) is pi