Question

$\underset{\mathbf{x}\mathbf{\rightarrow}\mathbf{0}}{\mathbf{\lim}}\frac{\mathbf{(1}\mathbf{-}\mathbf{\cos}\mathbf{2}\mathbf{x)}\mathbf{\sin}\mathbf{5}\mathbf{x}}{\mathbf{x}^{\mathbf{2}}\mathbf{\sin}\mathbf{3}\mathbf{x}}\mathbf{=}$

• A. $\frac{10}{3}$
• B. $\frac{3}{10}$
• C. $\frac{6}{5}$
• D. $\frac{5}{6}$

Answer 1

Answer: (A)

$\frac{10}{3}$

Answer 2

$\lim_{x \rightarrow 0}\frac{2\sin^{2}x\sin 5x3x5x}{x^{2}\sin 3x3x5x}$

= $\lim_{x \rightarrow 0}\frac{2\sin^{2}x}{x^{2}}.\frac{3x}{\sin 3x}.\frac{\sin 5x}{5x}.\frac{5x}{3x}$ = $2.\frac{5}{3} = \frac{10}{3}$.