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Limits Continuity And Differentiability

MHT CET 2025 21st April Evening Shift

MCQ+2 / -02025

If $f(x)= \begin{cases}\frac{8^x-4^x-2^x+1^x}{x^2}, & \text { if } x>0 \\ \mathrm{e}^x \sin x+\mathrm{i} x+\lambda \log 4, & \text { if } x \leqslant 0, \mathrm{i} \in \mathbb{R}\end{cases}$ continuous at $x=0$, then the value of $500 \mathrm{e}^\lambda$ is

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