A) If \[f(x)\] is not continuous at \[x=a\], then it is not differentiable at \[x=a\]
B) If \[f(x)\] is continuous at \[x=a\], then it is differentiable at \[x=a\]
C) If \[f(x)\] and \[g(x)\] are differentiable at \[x=a\], then \[f(x)+g(x)\] is also differentiable at \[x=a\]
D) If a function \[f(x)\] is continuous at \[x=a\], then \[\underset{x\to a}{\mathop{\lim }}\,f(x)\] exists
Correct Answer: B
Solution :
If a function \[f(x)\] is continuous at \[x=a,\] then it may or may not be differentiable at \[x=a\]. \[\therefore \] Option [b] is correct.
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