SATHEE: Limit Continuity and Differentiability 7 Question 18

Limit Continuity and Differentiability 7 Question 18

18. Which of the following functions is differentiable at $x = 0$ ?

(2001, 2M)

(a) $\cos (| x |) + | x |$

(b) $\cos (| x |) - | x |$

(d) $\sin (| x |) - | x |$

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Answer:

Correct Answer: 18. (b)

Solution:

Given, $x^{2} + y^{2} = 1$

On differentiating w.r.t. $x$ , we get

$\begin{aligned} 2 x + 2 y y^{'} & = 0 \\ \Rightarrow & x + y y^{'} & = 0 . \end{aligned}$

Again, differentiating w.r.t. $x$ , we get

$\begin{aligned} 1 + y^{'} y^{'} + y y^{''} = 0 \\ \Rightarrow 1 + {(y^{'})}^{2} + y y^{''} = 0 \end{aligned}$

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Limit Continuity and Differentiability 7 Question 18

18. Which of the following functions is differentiable at x=0 ?

Answer:

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18. Which of the following functions is differentiable at $x = 0$ ?