Question

$\underset{x\to 0}{lim}\frac{x^3\cot x}{1-\cos x}=?$

• A. $0$
• B. $1$
• C. $2$
• D. $-2$

Answer 1

Answer: (D)

$-2$

${lim}_{x\to 0}\frac{x^3\cot x}{1-\cot x}={lim}_{x\to 0}\frac{x^3\cos x}{\sin x.2{\sin }^2\frac{x}{2}}\frac{1}{2}\times {lim}_{x\to 0}\frac{\cos x}{\frac{\sin x}{x}\frac{{\sin }^2\frac{x}{2}\times \frac{1}{4}}{\frac{x^2}{4}}}=\frac{1}{2}\times \frac{1}{1\times 1\times \frac{1}{4}}=-2$