If and , where , which of the following statements is…

MATHEMATICS · Single correct · CBSE · Mathematics · Limits and Derivatives · Limits and Derivatives

Problem

If I1=lim⁡x→0tan⁡−1xx−sin⁡−1xxI_1=\lim_{x\to0}\sqrt{\frac{\tan^{-1}x}{x}-\frac{\sin^{-1}x}{x}} and I2=lim⁡x→0sin⁡−1xx−tan⁡−1xxI_2=\lim_{x\to0}\sqrt{\frac{\sin^{-1}x}{x}-\frac{\tan^{-1}x}{x}}, where ∣x∣<1|x|<1, which of the following statements is true? (1) Neither I1I_1 nor I2I_2 exists. (2) I1I_1 exists and I2I_2 does not exist. (3) I1I_1 does not exist and I2I_2 exists. (4) None of the above.

Related theory

Browse the problem library