Mathematics

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


ANSWER

$$\frac{1}{4}$$


View Full Answer

Its FREE, you're just one step away


Single Correct Medium Published on 17th 09, 2020
Next Question
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84
Enroll Now For FREE

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. $$\pi / 4$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Passage Hard
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 $$(0, 1)$$
Then answer the following question.

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer