Define (G(x)= _ 2 ^ g(x) 1 t^ 2 ,dt ) where (g(x)= cases x^ 2 ,&x 1 x+1,&x>1 cases

MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

Define G(x)=∫2g(x)1t2 dtG(x)=\int_{2}^{g(x)}\dfrac{1}{t^{2}}\,dt where g(x)={x2,x≤1sin⁡x+1,x>1.g(x)=\begin{cases}x^{2},&x\le 1\\ \sin x+1,&x>1\end{cases}. Compute the left-hand and right-hand derivatives of GG at x=1x=1 and state whether GG is differentiable there.

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