Q25·Section A (Section A)·25 of 60Differentiability at zero of two oscillating functionsLet f(x)={xsin2(1/x),x≠0, 0,x=0,andg(x)={x(sinx)sin(1/x),x≠0, 0,x=0.f(x)=\begin{cases}x\sin^2(1/x), & x\ne0,\ 0, & x=0,\end{cases}\quad\text{and}\quad g(x)=\begin{cases}x(\sin x)\sin(1/x), & x\ne0,\ 0, & x=0.\end{cases}f(x)={xsin2(1/x),x=0, 0,x=0,andg(x)={x(sinx)sin(1/x),x=0, 0,x=0. Then OptionsAfff is differentiable at 000 but ggg is NOT differentiable at 000Bggg is differentiable at 000 but fff is NOT differentiable at 000Cfff and ggg are both differentiable at 000DNEITHER fff NOR ggg is differentiable at 000Pick an option to check your answer.Show answerShow solution Report a problem with this question← Q24All questionsQ26 →Keyboard: A–D answer · S solution · ←/→ previous/next