If is continuous at

MATHEMATICS · Single correct · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

If f(x)={8x−4x−2x+1x2,x>0exsin⁡x+πx+λln⁡4,x≤0f(x)=\begin{cases}\frac{8^x-4^x-2^x+1}{x^2}, & x>0\\ e^x\sin x+\pi x+\lambda\ln 4, & x\leq 0\end{cases} is continuous at x=0x=0, then the value of λ\lambda is (a) 4log⁡e24\log_e 2 (b) 2log⁡e22\log_e 2 (c) log⁡e2\log_e 2 (d) none of these

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