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Integration by Partial Fractions

x→ 0lim[tanx+...

Question

$l i m x \to 0 {[tan (x + \frac{π}{4})]}^{1 / x} =$

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Solution

${lim}_{x \to 0} {(tan (x + \frac{π}{4}))}^{\frac{1}{x}} {lim}_{x \to 0} e^{\frac{tan (x + \frac{π}{4}) - 1}{x}} = {lim}_{x \to 0} e^{\frac{{sec}^{2} (x + \frac{π}{4})}{1}} = e^{2}$

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Similar questions

f (x) = ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} \begin{matrix} {(1 - | tan x |)}^{a / | tan x |}, & - \frac{π}{4} < x < 0 \end{matrix} \begin{matrix} b, & x = 0 \end{matrix} \begin{matrix} e^{\frac{sin 3 x}{sin 2 x}}, & 0 < x < \frac{π}{4} \end{matrix} \end{matrix}

x = 0

f (x) = \frac{1 - tan x}{4 x - π}, x \neq \frac{π}{4}, x \in [0, \frac{π}{4}]

f (x)

[0, \frac{π}{2}]

f (\frac{π}{4})

f (x) = \frac{1 - tan x}{4 x - π}

x \neq π / 4

x \in [0, \frac{π}{2}]

f (x)

[0, \frac{π}{2}]

f (\frac{π}{4})

f (x) = tan x, 0 \leq x \leq \frac{π}{4}

lim x \to 0 [\frac{tan x}{x}]

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