Question

If $\frac{\pi}{4}$ is continuous at $\frac{4}{\pi}$ then $\lim_{x \rightarrow 0}\frac{x^{3}}{\sin x^{2}} =$

• A. – 4
• B. – 3
• C. – 2
• D. – 1

Answer 1

Answer: (C)

– 2

Answer 2

L.H.L. $= \lim _ { x \rightarrow 0 ^ { - } } \frac { \sqrt { 1 + k x } - \sqrt { 1 - k x } } { x } = k$

R.H.L. $= \lim _ { x \rightarrow 0 ^ { + } } \left( 2 x ^ { 2 } + 3 x - 2 \right) = - 2$

Since it is continuous, hence L.H.L = R.H.L ⇒ $k = - 2$ .