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Recent questions tagged limits

6 votes
2 answers
183
TIFR CSE 2014 | Part A | Question: 16
Let $x_{0}=1$ and $x_{n+1}= \frac{3+2x_{n}}{3+x_{n}}, n\geq 0$. $x_{\infty}=\displaystyle \lim_{n\rightarrow \infty}x_{n}$ is $\left(\sqrt{5}-1\right) / 2$ $\left(\sqrt{5}+1\right) / 2$ $\left(\sqrt{13}-1\right) / 2$ $\left(-\sqrt{13}-1\right) / 2$ None of the above
Let $x_{0}=1$ and$x_{n+1}= \frac{3+2x_{n}}{3+x_{n}}, n\geq 0$.$x_{\infty}=\displaystyle \lim_{n\rightarrow \infty}x_{n}$ is$\left(\sqrt{5}-1\right) / 2$$\left(\sqrt{5}+1\...
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7 votes
3 answers
184
TIFR CSE 2012 | Part A | Question: 14
The limit $\displaystyle \lim_{n \rightarrow \infty} \left(\sqrt{n^{2}+n}-n\right)$ equals. $\infty$ $1$ $1 / 2$ $0$ None of the above
The limit $\displaystyle \lim_{n \rightarrow \infty} \left(\sqrt{n^{2}+n}-n\right)$ equals.$\infty$$1$$1 / 2$$0$None of the above
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2 votes
1 answer
185
Limit
Is the following statement correct? If yes, prove it. $\lim_{x \to 0^+} \log x = - \infty$
Is the following statement correct? If yes, prove it. $$\lim_{x \to 0^+} \log x = - \infty$$
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6 votes
1 answer
186
TIFR CSE 2011 | Part A | Question: 17
What is $\lim_{x \to 0} \frac{2^x-1}{x}$ $0$ $\log_2(e)$ $\log_e(2)$ $1$ None of the above
What is $$\lim_{x \to 0} \frac{2^x-1}{x}$$$0$$\log_2(e)$$\log_e(2)$$1$None of the above
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12 votes
4 answers
187
TIFR CSE 2011 | Part A | Question: 14
The limit $\lim_{x \to 0} \frac{d}{dx}\,\frac{\sin^2 x}{x}$ is $0$ $2$ $1$ $\frac{1}{2}$ None of the above
The limit $$\lim_{x \to 0} \frac{d}{dx}\,\frac{\sin^2 x}{x}$$ is$0$$2$$1$$\frac{1}{2}$None of the above
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3 votes
3 answers
188
TIFR2010-Maths-A-13
What is the value of $\lim_{x\to 0} \sin{\left (\frac1 x \right )}$ $1$ $0$ $\frac{1}{2}$ Does Not Exist
What is the value of $$\lim_{x\to 0} \sin{\left (\frac1 x \right )}$$$1$$0$$\frac{1}{2}$Does Not Exist
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15 votes
6 answers
189
TIFR CSE 2010 | Part A | Question: 7
The limit of $\dfrac{10^{n}}{n!}$ as $n \to \infty$ is. $0$ $1$ $e$ $10$ $\infty$
The limit of $\dfrac{10^{n}}{n!}$ as $n \to \infty$ is.$0$$1$$e$$10$$\infty$
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1 votes
3 answers
190
Please find the value of this limit
I have applied L'Hospital here. And result came up like this : $1 - \frac{1}{2} (y^{2} + y)^{-\frac{1}{2}} (2y+1)$ Then after applying limit value , result came as $-\infty$. Am I wrong ? Please correct me.
I have applied L'Hospital here. And result came up like this :$$1 - \frac{1}{2} (y^{2} + y)^{-\frac{1}{2}} (2y+1)$$Then after applying limit value , result came as $-\inf...
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1 votes
3 answers
191
Calculate the limit
$\lim_{x \to 0} \frac{\cos(x)-\log(1+x)-1+x}{\sin^2x} = ? $ Please explain the steps also
$$\lim_{x \to 0} \frac{\cos(x)-\log(1+x)-1+x}{\sin^2x} = ? $$Please explain the steps also
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0 votes
3 answers
192
select correct option for limit
$\lim_{x\rightarrow 0}\sin \left( \frac{1}{x}\right)$ (a) 1 (b) 0 (c) does not exist (d) none of these
$\lim_{x\rightarrow 0}\sin \left( \frac{1}{x}\right)$(a) 1(b) 0(c) does not exist(d) none of these
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1 votes
1 answer
193
calculate limit
$\lim_{x\rightarrow 0}\frac{ \sin x^{\circ}}{x}$
$\lim_{x\rightarrow 0}\frac{ \sin x^{\circ}}{x}$
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0 votes
1 answer
194
calculate limit
$\lim_{x\rightarrow 0} \left( \frac{1}{x^{2}} -\frac{1}{\sin^{2}x} \right)$
$\lim_{x\rightarrow 0} \left( \frac{1}{x^{2}} -\frac{1}{\sin^{2}x} \right)$
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0 votes
2 answers
195
calculate limit
$\lim_{\theta \rightarrow 0} \frac{ 1-\cos \theta }{ \theta \sin\theta }$
$\lim_{\theta \rightarrow 0} \frac{ 1-\cos \theta }{ \theta \sin\theta }$
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1 votes
2 answers
196
calculate limit
$\lim_{x\rightarrow 0} \frac{e^{x}-e^{\sin x}} {x-\sin x}$
$\lim_{x\rightarrow 0} \frac{e^{x}-e^{\sin x}} {x-\sin x}$
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0 votes
2 answers
197
calculate limit
$\lim_{x\rightarrow \infty }\frac{\sin x}{x}$
$\lim_{x\rightarrow \infty }\frac{\sin x}{x}$
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0 votes
2 answers
198
calculate limit
$\lim_{x\rightarrow 0} \frac{x^{x}-1}{x}$
$\lim_{x\rightarrow 0} \frac{x^{x}-1}{x}$
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0 votes
2 answers
199
calculate limit
$\lim_{x\rightarrow 0} \frac{6^{x}-2^{x}-3^{x}+1}{x^{2}}$
$\lim_{x\rightarrow 0} \frac{6^{x}-2^{x}-3^{x}+1}{x^{2}}$
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0 votes
1 answer
200
calculate limit
$\lim_{x\rightarrow 0}\frac{1^{x}+2^{x}+3^{x}+ \dots +n^{x}-n}{x}$
$\lim_{x\rightarrow 0}\frac{1^{x}+2^{x}+3^{x}+ \dots +n^{x}-n}{x}$
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1 votes
3 answers
201
calculate limit
$\lim_{x\rightarrow \infty }\left(4^{x}+5^{x}\right)^{1/x}$
$\lim_{x\rightarrow \infty }\left(4^{x}+5^{x}\right)^{1/x}$
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0 votes
1 answer
202
calculate limit
$\lim_{x\rightarrow \infty }x^{m}e^{-x}$ where m is +ve integer
$\lim_{x\rightarrow \infty }x^{m}e^{-x}$ where m is +ve integer
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0 votes
3 answers
203
calculate limit
$\lim_{x\rightarrow 0}\left ( \frac{a^{x}+b^{x}}{2} \right )^{^{\frac{1}{x}}}$
$\lim_{x\rightarrow 0}\left ( \frac{a^{x}+b^{x}}{2} \right )^{^{\frac{1}{x}}}$
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0 votes
2 answers
204
calculate limit
$\lim_{x\rightarrow \frac{\pi}{4}} (\tan x)^{\tan 2x}$
$\lim_{x\rightarrow \frac{\pi}{4}} (\tan x)^{\tan 2x}$
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1 votes
3 answers
205
calculate limit
$\lim_{x\rightarrow \frac{\pi}{2}}{( \sin x)}^{\tan x}$
$\lim_{x\rightarrow \frac{\pi}{2}}{( \sin x)}^{\tan x}$
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0 votes
4 answers
206
Limits
What is $\lim_{ x \to 0} (1-x)^{\frac{1}{x}}$ ? Also please explain the result?
What is $\lim_{ x \to 0} (1-x)^{\frac{1}{x}}$ ? Also please explain the result?
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32 votes
6 answers
207
GATE CSE 2015 Set 3 | Question: 9
The value of $\displaystyle \lim_{x \rightarrow \infty} (1+x^2)^{e^{-x}}$ is $0$ $\frac{1}{2}$ $1$ $\infty$
The value of $\displaystyle \lim_{x \rightarrow \infty} (1+x^2)^{e^{-x}}$ is$0$$\frac{1}{2}$$1$$\infty$
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26 votes
6 answers
208
GATE CSE 2015 Set 1 | Question: 4
$\displaystyle \lim_{x\rightarrow \infty } x^{ \tfrac{1}{x}}$ is $\infty $ $0$ $1$ Not defined
$\displaystyle \lim_{x\rightarrow \infty } x^{ \tfrac{1}{x}}$ is$\infty $$0$$1$Not defined
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31 votes
4 answers
209
GATE CSE 2014 Set 3 | Question: 47
The value of the integral given below is $\int \limits_0^{\pi} \: x^2 \: \cos x\:dx$ $-2\pi$ $\pi$ $-\pi$ $2\pi$
The value of the integral given below is$$\int \limits_0^{\pi} \: x^2 \: \cos x\:dx$$$-2\pi$$\pi$$-\pi$$2\pi$
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31 votes
5 answers
210
GATE CSE 2014 Set 3 | Question: 6
If $\int \limits_0^{2 \pi} |x \: \sin x| dx=k\pi$, then the value of $k$ is equal to ______.
If $\int \limits_0^{2 \pi} |x \: \sin x| dx=k\pi$, then the value of $k$ is equal to ______.
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