Lim_x → 0e^tan x 1/x = lim_x → 0e^tan x 1/tan x ×lim_x → 0tan x /x = log e × 1 = 1 ...

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Standard Limits to Remove Indeterminate Form

lim x → 0etan...

Question

${lim}_{x \to 0} \frac{e^{tan x} - 1}{x}$

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Solution

${lim}_{x \to 0} \frac{e^{tan x} - 1}{x} = {lim}_{x \to 0} \frac{e^{tan x} - 1}{tan x} \times {lim}_{x \to 0} \frac{tan x}{x} = l o g e \times 1 = 1$

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${lim}_{x \to 0} \frac{e^{tan x} - 1}{tan x}$

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