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GO Classes 2025 | Weekly Quiz 21 | Calculus | Question: 13

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The function
$$
f(x)= \begin{cases}e^x & \text { if } \quad x \leq 1 \\ m x+b & \text { if } \quad x>1\end{cases}
$$
is continuous and differentiable at $x=1$.

Find the value of $m-b?$

  1. $e$
  2. $-e$
  3. $\mathrm{e}-1$
  4. $1-e$
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1 Answer

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Detailed Video Solution: https://youtu.be/6aIuj2b2J38 

$m=e, b=0$.

Solve $\displaystyle\lim _{x \rightarrow 1^{-}} e^x=\displaystyle{}\lim _{x \rightarrow 1^{+}}(m x+b)$ and $\displaystyle\lim _{x \rightarrow 1^{-}} \frac{e^x-e}{x-1}=\lim _{x \rightarrow 1^{+}} \frac{m x+b-(m+b)}{x-1}$ for $m$ and $b$.

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