What is the limit as x approaches pi/4 of 7tan^{tan(2x)}(x) ?

The limit as x approaches pi/4 of 7tan^{tan(2x)}(x) is 7/e

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limit as x approaches pi/4 of 7tan^{tan(2x)}(x)

x \to \frac{π}{4} lim (7 tan^{t a n (2 x)} (x))

\frac{7}{e}

Decimal

2.57515 \dots

Solution steps

x \to \frac{π}{4} lim (7 tan^{t a n (2 x)} (x))

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= 7 \cdot x \to \frac{π}{4} lim (tan^{t a n (2 x)} (x))

Apply exponent rules

= 7 \cdot 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}

= 7 \cdot \frac{1}{e}

Simplify

7 \cdot \frac{1}{e} : \frac{7}{e}

= \frac{7}{e}

x \to - 1 lim (2^{1 + l n (x)})

x \to a lim (\frac{x + 4}{x - 3})

x \to - 5 lim (17)

x \to - \infty lim ((x)^{3})

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

What is the limit as x approaches pi/4 of 7tan^{tan(2x)}(x) ?
The limit as x approaches pi/4 of 7tan^{tan(2x)}(x) is 7/e