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

The limit as x approaches pi/4 of (tan(4x))/(4x-pi) is 1

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

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

1

Solution steps

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

Apply L'Hopital's Rule

: x \to \frac{π}{4} lim (\frac{sec ^{2} ( 4 x ) \cdot 4}{4})

= x \to \frac{π}{4} lim (\frac{sec ^{2} ( 4 x ) \cdot 4}{4})

Plug in the value

x = \frac{π}{4}

= \frac{sec ^{2} ( 4 \cdot \frac{π}{4} ) \cdot 4}{4}

Simplify

\frac{sec ^{2} ( 4 \cdot \frac{π}{4} ) \cdot 4}{4} : 1

= 1

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- y^{^{'''}} - y^{^{''}} + 5 y^{^{''}} - 3 = 0

What is the limit as x approaches pi/4 of (tan(4x))/(4x-pi) ?
The limit as x approaches pi/4 of (tan(4x))/(4x-pi) is 1