Given below are two statements: Statement I : \lim_{x ightarrow 0} ( { an ^{-1} x+\log _e \sqrt{\frac{1+x}{1-x}}-2 x}/{x^5}) =\frac{2}{5} Statement II : \lim_{x ightarrow 1} (x^{\frac{2}{1-x}}) =\frac{1}{e^2} In the light of the above statements, choose the correct answer from the options given below [8 Apr 2025 Shift 2]

Question

Given below are two statements: Statement I : \lim_{x ightarrow 0} ( {	an ^{-1} x+\log _e \sqrt{\frac{1+x}{1-x}}-2 x}/{x^5}) =\frac{2}{5} Statement II : \lim_{x ightarrow 1} (x^{\frac{2}{1-x}}) =\frac{1}{e^2} In the light of the above statements, choose the correct answer from the options given below [8 Apr 2025 Shift 2]

Examsnet · Accepted Answer

Correct Answer is : Both Statement I and Statement II are true

Limits, Continuity and Differentiability Part 3