What is the limit as x approaches pi/4 of (tan(x))^{tan(2x)} ?

The limit as x approaches pi/4 of (tan(x))^{tan(2x)} is 1/e

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limit as x approaches pi/4 of (tan(x))^{tan(2x)}

x \to \frac{π}{4} lim ((tan (x))^{t a n (2 x)})

\frac{1}{e}

Decimal

0.36787 \dots

Solution steps

x \to \frac{π}{4} lim ((tan (x))^{t a n (2 x)})

Apply exponent rules

= x \to \frac{π}{4} lim (e^{t a n (2 x) l n (t a n (x))})

Apply the Limit Chain Rule:

\frac{1}{e}

= \frac{1}{e}

x \to 5 + lim (ln (x^{2} - 25))

y = x 16 - x^{2}

\frac{d}{d x} (ln (cos^{2} (x)))

y^{^{''}} + y = 3 x^{2}

\int_{0}^{\frac{π}{8}} cos (4 x) d x

What is the limit as x approaches pi/4 of (tan(x))^{tan(2x)} ?
The limit as x approaches pi/4 of (tan(x))^{tan(2x)} is 1/e