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If $f$ is differentiable function, the value of $\lim_{h \to 0} \frac{{[f (x + h)]}^{2} - {[f (x)]}^{2}}{2 h}$ is equal to

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f(x)f(x)

f(x)2

12f(x)2

f'x2−fx22

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detailed solution

Correct option is A

By definition, the given limit=12ddxfx2=12.2fxfx=fxfxHence (1) is the correct answer.

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If f is differentiable function, the value of limh→0fx+h2−fx22h is equal to

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If $f$ is differentiable function, the value of $\lim_{h \to 0} \frac{{[f (x + h)]}^{2} - {[f (x)]}^{2}}{2 h}$ is equal to