SATHEE: Application of Derivatives 2 Question 25

Application of Derivatives 2 Question 25

####25. Match the conditions/expressions in Column I with statements in Column II.

Let the functions defined in Column I have domain $(- π / 2, π / 2)$ .

Column I
A. $x + \sin x$	p. increasing
B. $\sec x$	q. decreasing
	r. neither increasing nor decreasing

Analytical & Descriptive Questions

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Answer:

Correct Answer: 25. (c)

Solution:

$\frac{d}{d x} (x + \sin x) = 1 + \cos x = 2 \cos^{2} \frac{x}{2} > 0$ for $- \frac{π}{2} < x < \frac{π}{2}$ .

Therefore, $x + \sin x$ is increasing in the given interval. Therefore, $(A) \to (p)$ is the answer.

Again, $\frac{d}{d x} (\sec x) = \sec x \tan x$ which is $> 0$ for $0 < x < π / 2$ and

$< 0 for \frac{- π}{2} < x < 0$

Therefore, sec $x$ is neither increasing nor decreasing in the given interval. Therefore, $(B) \to (r)$ is the answer.

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Application of Derivatives 2 Question 25

Analytical & Descriptive Questions

Answer:

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