Mathematics

# Find its:-$\mathop {Lt}\limits_{x \to \infty } \left( {\frac{{1 + {2^4} + {3^4} + ......{n^4}}}{{{n^5}}}} \right) - \mathop {Lt}\limits_{x \to \infty } \left( {\frac{{1 + {2^3} + {3^3} + ......{n^3}}}{{{n^5}}}} \right) =$

$\frac{1}{4}$

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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
The value of $\displaystyle \int^{\pi/4}_{-\pi /4} \dfrac{dx}{sec^2x(1-sinx)}$ is
• A. $\pi$
• B. $\pi / 2$
• C. $2 \pi$
• D. $\pi / 4$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
$\int { \dfrac { ln\left( lnx \right) }{ xlnx } } dx,\left( x>0 \right)$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
If $I=\int \dfrac{dx}{\sin^{4}{x}+\cos^{4}{x}}$, then Find out $I$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Hard
$\int _{ 0 }^{ k }{ \dfrac { 1 }{ 2+{ 8x }^{ 2 } } dx=\dfrac { \pi }{ 16 } }$, find the value of $K$.

Given that for each $\displaystyle a \in (0, 1), \lim_{h \rightarrow 0^+} \int_h^{1-h} t^{-a} (1 -t)^{a-1}dt$ exists. Let this limit be $g(a)$
In addition, it is given that the function $g(a)$ is differentiable on $(0, 1)$