Mathematics

# $\lim_{x\rightarrow \infty }\left [ \left ( 1+\frac{1}{n^{2}}^{\frac{2}{n}^{2}} \right )\left ( 1+\frac{2^{2}}{n^{2}}^{\frac{4}{n^{2}}} \right )......\left ( 1+\frac{n^{2}}{n^{2}}^{\frac{2n}{n^{2}}} \right ) \right ]equals$

$\frac{2}{e}$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

#### Realted Questions

Q1 Single Correct Medium
$\displaystyle \int_{\sin \theta}^{\cos \theta} f(x \tan \theta) d x\left(\text { where } \theta \neq \dfrac{n \pi}{2}, n \in I\right)$ is equal to
• A. $-\tan \theta \int_{\cos \theta}^{\sin \theta} f(x) d x$
• B. $\sin \theta \int_{1}^{\tan \theta} f(x \cos \theta) d x$
• C. $\frac{1}{\tan \theta} \int_{\sin \theta}^{\sin \theta \tan \theta} f(x) d x$
• D. $-\cos \theta \int_{1}^{\tan \theta} f(x \sin \theta) d x$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
$\int (sin^4x-cos^4x)dx$ is equal to
• A. $-\frac{cos2x}{2}+c$
• B. $\frac{sin2x}{2}+c$
• C. $\frac{cos2x}{2}+c$
• D. $-\frac{sin2x}{2}+c$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
By using the properties of definite integrals, evaluate the integral  $\displaystyle \int_0^{\tfrac {\pi}{2}}\cfrac {\sqrt {\sin x}}{\sqrt {\sin x}+\sqrt {\cos x}}dx$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Hard
Solve:$\int\dfrac{dx}{(x^2+1)^3}$

$\int \frac{2x^{2}}{3x^{4}2x} dx$