Question

$\underset{x\to 0}{\lim }\frac{x\cot \left(4x\right)}{{\sin }^{2}x{\cot }^2\left(2x\right)}$ is equal to :

• A. 2
• B. 0
• C. 4
• D. 1

Answer 1

Answer: (D)

${\lim }_{x\to 0}\frac{x{\tan }^{2}2x}{\tan 4x{\sin }^{2}x}={\lim }_{x\to 0}\frac{x\left(\frac{{\tan }^{2}2x}{4x^2}\right)4x^2}{\left(\frac{\tan 4x}{4x}\right)4x\left(\frac{{\sin }^{2}x}{x^2}\right)x^2}=1$