Mathematics

$\lim_\limits{n\to \infty}\left(\frac{(n+1)(n+2)......3n}{2^{2n}}\right)^{\frac{1}{n}}$ is equal to:

$\dfrac{27}{e^2}$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

Realted Questions

Q1 Single Correct Medium
The  value of the integral $\int\int xy(x+y)dx {\,}dy$ over the area between $y=x^2$ and $y=x$ is
• A. $\dfrac{47}{56}$
• B. $\dfrac{33}{56}$
• C. $\dfrac{23}{56}$
• D. $\dfrac{3}{56}$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
Evaluate : $\int \dfrac { sec x}{( sec x + tan x ) } dx$
• A. $tan x+ sec x+ C$
• B. $-tan x + sec x + C$
• C. $-tan x - sec x + C$
• D. $tan x -sec x + C$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Hard
Evaluate:
$\int { \sqrt { 4-{ x }^{ 2 } } } dx\quad$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Hard
Evaluate: $\displaystyle \int { \dfrac { x\sqrt { x } .dx }{ \sqrt { 1-{ x }^{ 5 } } } }$
• A. $\dfrac { 2 }{ 5 } x\sin ^{ -1 } ({ x } ^{ \frac { 5 }{ 2 } })+c$
• B. $\dfrac { 1 }{ 5 } x\sin ^{ -1 }({ x } ^{ \frac { 3 }{ 2 } })+c$
• C. $\dfrac { 1 }{ 3 } x\sin ^{ -1 }({ x } ^{ \frac { 3 }{ 2 } })+c$
• D. $\dfrac { -2 }{ 5 }\sin ^{ -1 }(\sqrt{1-{ x }^5 })+c$

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Hard
If $f(a+b-x)=f(x)$ then $\int_{a}^{b}xf\left ( x \right )dx$ equals
• A. $\displaystyle \frac{b-a}{2}\int_{a}^{b}f\left ( x \right )dx$
• B. $\displaystyle \frac{a+b}{2}\int_{a}^{b}f\left ( a+bx \right )dx$
• C. $\displaystyle \frac{a+b}{2}\int_{a}^{b}f\left ( b-x \right )dx$
• D. $\displaystyle \frac{a+b}{2}\int_{a}^{b}f\left ( x \right )dx$