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SSC Pure Mathematics QUESTION #4121
Question 1
By Mean Value Theorem on $f(x) = e^x$, for $x > 0$, there exists $c \in (0, x)$ such that:
  • $e^x - 1 = e^c \cdot x$✔️
  • $e^x - 1 = x$
  • $e^x = 1 + cx$
  • $\frac{e^x - 1}{x} = c$
Correct Answer Explanation
MVT: $\frac{f(x) - f(0)}{x - 0} = f'(c) = e^c$. So $\frac{e^x - 1}{x} = e^c$, giving $e^x - 1 = xe^c$.