Question

If f(x) = sin^–1$\lim_{x \rightarrow 0}\left( \frac{\int_{0}^{x^{2}}{\sec^{2}tdt}}{x\sin x} \right)$, then f(x) is differentiable on :

• A. [–1, 1]
• B. R – {–1, 1}
• C. R – (–1, 1)
• D. None of these

Answer 1

Answer: (B)

R – {–1, 1}

Answer 2

f(x) = sin^–1

= $\frac { 1 + x ^ { 2 } } { \sqrt { \left( 1 + x ^ { 2 } \right) ^ { 2 } - 4 x ^ { 2 } } } \times \frac { 2 + 2 x ^ { 2 } - 4 x ^ { 2 } } { \left( 1 + x ^ { 2 } \right) ^ { 2 } }$

not defined when (1 + x²)² – 4x² = 0

x = ± 1

Differential at R – {–1, 1}