SATHEE: Limit Continuity and Differentiability 1 Question 7

Limit Continuity and Differentiability 1 Question 7

8. $lim_{x \to π / 2} \frac{\cot x - \cos x}{(π - 2 x)^{3}}$ equals

(2017 Main)

(a) $\frac{1}{24}$

(b) $\frac{1}{16}$

(d) $\frac{1}{4}$

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Answer:

Correct Answer: 8. (b)

Solution:

Given, $p = lim_{x \to 0^{+}} {(1 + \tan^{2} \sqrt{x})}^{\frac{1}{2 x}} (1^{\infty}$ form $)$

$\begin{aligned} = e^{lim_{x \to 0^{+}} \frac{\tan^{2} \sqrt{x}}{2 x}} = e^{\frac{1}{2} lim_{x \to 0^{+}} {\frac{\tan \sqrt{x}}{\sqrt{x}}}^{2}} = e^{\frac{1}{2}} \\ ∴ \log p = \log e^{\frac{1}{2}} = \frac{1}{2} \end{aligned}$

Limit Continuity and Differentiability 1 Question 7

8. $lim_{x \to π / 2} \frac{\cot x - \cos x}{(π - 2 x)^{3}}$ equals

Answer:

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Limit Continuity and Differentiability 1 Question 7

8. limx→π/2cot⁡x−cos⁡x(π−2x)3 equals

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

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NCERT Exercise Video Solution

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8. $lim_{x \to π / 2} \frac{\cot x - \cos x}{(π - 2 x)^{3}}$ equals