Let the function $$f(x)=sin3$$⁡$$x2x$$∀x≠$$00$$∀$$x=0$$

Correct option is 4Continuous and differentiable at x = 0

Questions

$Let the function f (x) = \{\begin{array}{cc} \frac{\sin^{3} x^{2}}{x} & \forall x \neq 0 \\ 0 & \forall x = 0 \end{array}$

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is continuous but not derivable at x=0 2) 3)

Neither continuous nor differentiable at x = 0

continuous but not differentiable at x = 1

Continuous and differentiable at x = 0

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detailed solution

Correct option is D

Ltx→0 fx=Ltx→0 sinx2x2xsin2x2=Ltx→0 sinx2x2.Ltx→0 xsin2x2=0=f(0) And L.H.D at x=0 is Lth→0⁡f(0+h)−0h=sin3⁡h2h−0h=0R.H.D = 0∴f is differentiable at x=0

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Let the function f(x)=sin3⁡x2x∀x≠00∀x=0

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$Let the function f (x) = \{\begin{array}{cc} \frac{\sin^{3} x^{2}}{x} & \forall x \neq 0 \\ 0 & \forall x = 0 \end{array}$