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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Limits

NTA Abhyas 2020 · Mathematics · Limits

The value of _ x → 0 (sec x + tan x) ^ (1)/(x) is equal to

The value of $\lim_{x \to 0}{\left(sec x + tan x\right)}^{\dfrac{1}{x}} is equal to

Options

  1. Aee
  2. Be2e^{2}
  3. Ce−1e^{- 1}
  4. D11

Correct answer

A. ee

Step-by-step solution

lim⁡x→0(secx+tanx)1x\lim_{x \to 0}{\left(sec x + tan x\right)}^{\dfrac{1}{x}} (1∞{1}^{\infty} form)
= e^{\lim_{x \to 0}\dfrac{1}{x}\left(sec x + tan x - 1\right)} = e^{\lim_{x \to 0}\left(\dfrac{1 + sin x - cos x}{xcos x}\right)} = e^{\lim_{x \to 0} \left(\dfrac{\text{ cos } x +\text{ sin } x}{-\text{ xsin } x +\text{ cos } x}\rright)}\left(byL ' Hospitalrule\right)<br/>=<br />=e\dfrac{1 + 0}{0 + 1} =ee
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