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Limits Continuity And Differentiability

MHT CET 2025 21st April Morning Shift

MCQ+2 / -02025

If $f(x)= \begin{cases}\frac{8^x-4^x-2^x+1}{x^2}, & \text { if } x>0 \\ e^x \sin x+x+\lambda \log 4, & \text { if } x \leqslant 0\end{cases}$


is continuous at $x=0$ then the value of $1000 \mathrm{e}^\lambda=$

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