If the function f(x) has LHD and RHD at $x_{0}$ , which are finite and equal, then f(x) is differentiable at $x_{0}$ , always.

True

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False

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Solution

The correct option is A True
Fit is not sufficient for LHD and RHD to be equal rthe function f(x) must be continuous at $x_{0}$ .

For example, consider the function $f (x) = \frac{x^{2}}{x}$ .

LHD at x=0 is 1

RHD at x=0 is 1

But f(x) is not difined at x=0 i.e., f(x) is discontinuous at z=0 it is not differentiable at x=0

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If the function f(x) has LHD and RHD at x0, which are finite and equal, then f(x) is differentiable at x0, always.

The correct option is A TrueFit is not sufficient for LHD and RHD to be equal rthe function f(x) must be continuous at x0. For example, consider the function f(x)=x2x. LHD at x=0 is 1 RHD at x=0 is 1 But f(x) is not difined at x=0 i.e., f(x) is discontinuous at z=0 it is not differentiable at x=0

If the function f(x) has LHD and RHD at $x_{0}$ , which are finite and equal, then f(x) is differentiable at $x_{0}$ , always.