Given below are two statements: Statement I : \lim_{x \rightarrow 0} ( {\tan ^{-1} x+\log _e \sqrt{\frac{1+x}{1-x}}-2 x}/{x^5}) =\frac{2}{5} Statement II : \lim_{x \rightarrow 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]

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

Statement I is false but Statement II is true

Both Statement I and Statement II are false

Both Statement I and Statement II are true

Statement I is true but Statement II is false

Limits, Continuity and Differentiability Part 3

Section: Mathematics

Question : 12 of 69

Marks: +1, -0

Given below are two statements:
Statement I:

lim

x⟶0

(‌

tan−1x+loge√

1+x

1−x

−2x

)=‌

Statement II:

lim

x⟶1

(x‌

1−x

)=‌

In the light of the above statements, choose the correct answer from the options given below

[8 Apr 2025 Shift 2]

Go to Question:

Prev Question

Next Question