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  • <img alt="f(x)=\left\{\begin{array}{l} \frac{\sin x^2}{x}, x \neq 1, \text { then at } x=0 \\ 0, x=0 \end{array}\right." src="https://entrancecorner.oncodecogs.com/gif.latex?f%28x%29%3D%5Cleft%5C%7

f(x)=\left\{\begin{array}{l} \frac{\sin x^2}{x}, x \neq 1, \text { then at } x=0 \\ 0, x=0 \end{array}\right.

Option: 1

f(x) is continuous but non−differentiable


Option: 2

f(x) is differentiable


Option: 3

f(x) is discontinuous at x = 0


Option: 4

none of these


Answers (1)

best_answer

f^{\prime}(0)=\lim _{h \rightarrow 0} \frac{f(h)-f(0)}{h}=\lim _{h \rightarrow 0} \frac{\sin h^2}{h^2}=1

Thus f(x) is differentiable at x = 0 at hence also continuous at x = 0

Posted by

vinayak

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