Question

Solve this using L Hospital rule:
${lim}_{x\to a}\frac{sin{x}^{100}-sin{a}^{100}}{sinx-sina}$

Answer 1

${lim}_{x\to a}\frac{sin{x}^{100}-sin{a}^{100}}{sinx-sina}$
Now, applying L'Hospital' rule
$\Rightarrow {lim}_{x\to a}\frac{cos{x}^{100}.100x^{99}}{cosx}=\frac{100.a^{99}.cos{a}^{100}}{cosa}$
$=\frac{100a^{99}}{cosa}.cos{a}^{100}$