Register

TIFR-2019-Maths-A: 6

• edited by
663 views
0 votes
0 votes

The limit

$$\underset{n\rightarrow \infty }{\lim}\:n^{2}\int_{0}^{1}\:\frac{1}{\left ( 1+x^{2} \right )^{n}}\:dx$$

is equal to

  1. $1$
  2. $0$
  3. $+\infty$
  4. $1/2$
• edited by
User Avatar

Please log in or register to answer this question.

Voting & Accepting an answer helps improve the community
Answer:
← PreviousNext →
← Previous in categoryNext in category →

Related questions

0 votes
0 votes
0 answers
1
soujanyareddy13 asked Aug 29, 2020
140 views
TIFR-2019-Maths-B: 6
True/False Question : For any $n\geq 2$, there exists an $n\times n$ real matrix $A$ such that the set $\left \{ A^{p} \mid p\geq 1 \right \}$ spans the $\mathbb{R}$-vector space $M_{n}\left ( \mathbb{R} \right )$.
True/False Question :For any $n\geq 2$, there exists an $n\times n$ real matrix $A$ such that the set $\left \{ A^{p} \mid p\geq 1 \right \}$ spans the $\mathbb{R}$-vecto...
User Avatar
0 votes
0 votes
0 answers
2
soujanyareddy13 asked Aug 29, 2020
174 views
TIFR-2019-Maths-A: 1
The following sum of numbers (expressed in decimal notation) $1+11+111+\cdots +\underset{n}{\underbrace{11\dots1}}$ is equal to $\left ( 10^{n+1}-10-9n \right )/81$ $\left ( 10^{n+1}-10+9n \right )/81$ $\left ( 10^{n+1}-10-n \right )/81$ $\left ( 10^{n+1}-10+n \right )/81$
The following sum of numbers (expressed in decimal notation)$$1+11+111+\cdots +\underset{n}{\underbrace{11\dots1}}$$is equal to$\left ( 10^{n+1}-10-9n \right )/81$$\left ...
User Avatar
0 votes
0 votes
0 answers
3
soujanyareddy13 asked Aug 29, 2020
170 views
TIFR-2019-Maths-A: 2
For $n\geq 1$, the sequence $\left \{ x_{n} \right \}^{\infty }_{n=1},$ where: $x_{n}=1+\frac{1}{\sqrt{2}}+\dots+\frac{1}{\sqrt{n}}-2\sqrt{n}$ is decreasing increasing constant oscillating
For $n\geq 1$, the sequence $\left \{ x_{n} \right \}^{\infty }_{n=1},$ where:$$x_{n}=1+\frac{1}{\sqrt{2}}+\dots+\frac{1}{\sqrt{n}}-2\sqrt{n}$$isdecreasingincreasingconst...
User Avatar
Link Copied!