SATHEE: Limit Continuity and Differentiability 7 Question 33

Limit Continuity and Differentiability 7 Question 33

34. If $f (x) = - \cos x, - \frac{π}{2} < x \leq 0$ , then

$x - 1, 0 < x \leq 1$

$\ln x, x > 1$

(a) $f (x)$ is continuous at $x = - \frac{π}{2}$

(2011)

(b) $f (x)$ is not differentiable at $x = 0$

(d) $f (x)$ is differentiable at $x = - \frac{3}{2}$

Show Answer

Answer:

Correct Answer: 34. True

Solution:

Given, $h (x) = [f (x)]^{2} + [g (x)]^{2}$

$\begin{aligned} \Rightarrow h^{'} x & = 2 f (x) \cdot f^{'} (x) + 2 g (x) \cdot g^{'} (x) \\ = 2 [f (x) \cdot g (x) - g (x) \cdot f (x)] \\ = 0 [∵ f^{'} (x) = g (x) and g^{'} (x) = - f (x)] \end{aligned}$

$∴ h (x)$ is constant.

$\Rightarrow h (10) = h (5) = 11$

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Limit Continuity and Differentiability 7 Question 33

34. If f(x)=−cos⁡x,−π2<x≤0, then

Answer:

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34. If $f (x) = - \cos x, - \frac{π}{2} < x \leq 0$ , then