MCQ
$\mathop {\lim }\limits_{x \to 0} \frac{{{e^{\alpha \;x}} - {e^{\beta \;x}}}}{x} = $
- A$\alpha + \beta $
- B$\frac{1}{\alpha } + \beta $
- C${\alpha ^2} - {\beta ^2}$
- ✓$\alpha - \beta $
$ = \mathop {\lim }\limits_{x \to 0} \,\frac{{{e^{\alpha x}} - 1}}{{x}} - \mathop {\lim }\limits_{x \to 0} \,\frac{{{e^{\beta x}} - 1}}{{ x}}$
$ = \alpha \mathop {\lim }\limits_{x \to 0} \,\frac{{{e^{\alpha x}} - 1}}{{\alpha x}} - \beta \mathop {\lim }\limits_{x \to 0} \,\frac{{{e^{\beta x}} - 1}}{{\beta x}}$
$ = \alpha .1 - \beta .1 = \alpha - \beta .$
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