Aspire Faculty ID #15258 · Topic: JAMIA MCA 2016 · Just now
JAMIA MCA 2016

If $\displaystyle \lim_{x \to a} \frac{x^{\alpha} - x^{a}}{x - a} = -1$, then $\alpha$ is equal to …

Solution

Limit $\Rightarrow \dfrac{d}{dx}x^{\alpha}=\alpha x^{\alpha-1}$. At $x=a$, $\alpha a^{\alpha-1}=-1$. If $a=1$, $\alpha=-1$.
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