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Recent questions tagged limits

2 votes
1 answer
151
Numerical Aptitude
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1 votes
2 answers
152
Targate
How to solve this?
How to solve this?
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0 votes
2 answers
153
limit
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1 votes
1 answer
154
math
someone plz give solution
someone plz give solution
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2 votes
2 answers
155
GATE [Math]
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2 votes
2 answers
156
Limits
How to slove this $\lim_{n\rightarrow \infty }\left ( 10^{n}+n^{20} \right )/n!$
How to slove this$\lim_{n\rightarrow \infty }\left ( 10^{n}+n^{20} \right )/n!$
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2 votes
1 answer
157
Limit
Calculate the limit $\lim_{x \rightarrow 1-} \sqrt[3]{x+1} \: ln \: (x+1)$ 1 0 2 Does not exist
Calculate the limit$\lim_{x \rightarrow 1-} \sqrt[3]{x+1} \: ln \: (x+1)$102Does not exist
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3 votes
2 answers
158
limits
what is the value of $\textstyle \lim_{x \to 2}\frac{x-2}{\log(x-1)}$
what is the value of$\textstyle \lim_{x \to 2}\frac{x-2}{\log(x-1)}$
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2 votes
2 answers
159
Gate 2014 CE Set 2
The expression $\lim_{a \to 0}\frac{x^{a}-1}{a}$ is equal to (A)$\log x$ (B)0 (c)$x\log x$ (D)$\infty$
The expression $\lim_{a \to 0}\frac{x^{a}-1}{a}$ is equal to (A)$\log x$ (B)0 (c)$x\log x$ (D)$\infty$
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0 votes
1 answer
161
limits
$\lim_{x \to 0}x\log _x a$ $(A)0$ $(B)\log_ae$ $(C)1$ $(D)\log a$
$\lim_{x \to 0}x\log _x a$$(A)0$ $(B)\log_ae$$(C)1$ ...
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10 votes
1 answer
162
ISRO2016-3
$\displaystyle{}\lim_{x\rightarrow 0}\frac{\sqrt{1+x}-\sqrt{1-x}}{x}$ is given by $0$ $-1$ $1$ $\frac{1}{2}$
$\displaystyle{}\lim_{x\rightarrow 0}\frac{\sqrt{1+x}-\sqrt{1-x}}{x}$ is given by$0$$-1$$1$$\frac{1}{2}$
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0 votes
3 answers
163
Limit
Can we calculate. $\textstyle \lim_{n \to \infty}\frac{2^{n}}{3^{n}}$ if yes then what is the value.
Can we calculate. $\textstyle \lim_{n \to \infty}\frac{2^{n}}{3^{n}}$ if yes then what is the value.
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0 votes
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164
Calculus
​​If $a=\Sigma_{n=0}^{\infty} \frac{x^{3n}}{(3n)!}, \: b=\Sigma_{n=1}^{\infty} \frac{x^{3n-2}}{(3n-2)!} $ and $c=\Sigma_{n=1}^{\infty} \frac{x^{3n-1}}{(3n-1)!} $, then the value of $(a^3+b^3+c^3-3abc)$ is 1 0 -1 -2
​​If $a=\Sigma_{n=0}^{\infty} \frac{x^{3n}}{(3n)!}, \: b=\Sigma_{n=1}^{\infty} \frac{x^{3n-2}}{(3n-2)!} $ and $c=\Sigma_{n=1}^{\infty} \frac{x^{3n-1}}{(3n-1)!} $, the...
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2 votes
1 answer
165
calculus
$\lim_{x \to \infty}\left (\frac{1}{1-x^{2}} + \frac{2}{1-x^{2}}+\dots+\frac{x}{1-x^{2}}\right )$ is equal to (a) $0$ (b) $-1/2$ (c) $1/2$ (d) None of the above
$\lim_{x \to \infty}\left (\frac{1}{1-x^{2}} + \frac{2}{1-x^{2}}+\dots+\frac{x}{1-x^{2}}\right )$ is equal to(a) $0$(b) $-1/2$(c) $1/2$(d) None of the above
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1 votes
1 answer
166
Limit of Logarithematic and Exponentials
Find the value of the following limit $\lim_{x \to 0} x^{\sin x}$ ... $0 \cdot \infty$ form now? How do I proceed further?
Find the value of the following limit $$\lim_{x \to 0} x^{\sin x}$$My attempt:$$\begin{align*}\text{Let: }\\y &= \lim_{x \to 0} \Bigl [ x^{\sin x} \Bigr ]\\[1em]\text{The...
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26 votes
4 answers
167
GATE CSE 2016 Set 1 | Question: 3
$\lim _{x\rightarrow 4}\frac{\sin(x-4)}{x-4}=\_\_\_\_\_\_\_\_\_\_\_\_$
$$\lim _{x\rightarrow 4}\frac{\sin(x-4)}{x-4}=\_\_\_\_\_\_\_\_\_\_\_\_$$
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0 votes
1 answer
169
How to solve this using logarithms on both sides?
How to use log and solve this qn?
How to use log and solve this qn?
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2 votes
2 answers
170
limits
Find the value of: $\lim_{\theta \to \pi/2} \left ( 1 - 5 \cot\theta \right )^{\tan\theta}$ $e^{5}$ $e^{-5}$ $e^{1/5}$ $e^{-1/5}$
Find the value of: $$\lim_{\theta \to \pi/2} \left ( 1 - 5 \cot\theta \right )^{\tan\theta}$$$e^{5}$ $e^{-5}$ $e^{1/5}$ $e^{-1/5}$
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2 votes
1 answer
171
limit
Value of $\lim_{x \to 0} \frac{x^2 \sin \left(\frac{1}{x}\right)} {\sin x}$ is
Value of $\lim_{x \to 0} \frac{x^2 \sin \left(\frac{1}{x}\right)} {\sin x}$ is
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3 votes
2 answers
173
Limits
Please give the answer with full solution.
Please give the answer with full solution.
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2 votes
2 answers
174
The value of a and b such that
$\lim_{x \to 0} \frac{ a sin ^2x + b log ( cos x) }{ x^4} = \frac{1}{2}$ a) - 1, -2 b) 1, 2 c) -1,2 d) 1,-2
$\lim_{x \to 0} \frac{ a sin ^2x + b log ( cos x) }{ x^4} = \frac{1}{2}$a) - 1, -2 b) 1, 2c) -1,2 d) 1,-2
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3 votes
3 answers
175
solve calculate the limit
$\lim_{n \to \infty} \left [ \frac{1}{(1+n)} + \frac{1}{(2+n)} + - - - - - + \frac{1}{(n+n)} \right ]$ a) $log 2$ b) $2$ c) $\frac{1}{2}$ d) $\Pi /4$
$\lim_{n \to \infty} \left [ \frac{1}{(1+n)} + \frac{1}{(2+n)} + - - - - - + \frac{1}{(n+n)} \right ]$a) $log 2$ b) $2$c) $\frac{1}{2}$ ...
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4 votes
2 answers
176
Limits 1raise to infinite
$\lim_{x \rightarrow \infty} \left(\frac{x^{2} + 5x +3}{x^{2} + x + 2}\right)^{x}$
$\lim_{x \rightarrow \infty} \left(\frac{x^{2} + 5x +3}{x^{2} + x + 2}\right)^{x}$
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3 votes
2 answers
177
Limits Indeterminate forms
$\lim_{x \rightarrow 0^{+}} x^{\frac{1}{\ln x}}$
$\lim_{x \rightarrow 0^{+}} x^{\frac{1}{\ln x}}$
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3 votes
1 answer
178
Limits indeterminate form
$\lim_{x \rightarrow \infty} \left(\frac{x + 4}{x + 3}\right)^{x + 1}$
$\lim_{x \rightarrow \infty} \left(\frac{x + 4}{x + 3}\right)^{x + 1}$
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2 votes
2 answers
179
Solve : calculate the limit
Calculate the limit $\lim_{x\rightarrow 1^- } \sqrt[3]{x+1}\: ln(x+1)$ (A) $1$ (B) $0$ (C) $2$ (D) Does not exist
Calculate the limit $$\lim_{x\rightarrow 1^- } \sqrt[3]{x+1}\: ln(x+1)$$(A) $1$(B) $0$(C) $2$(D) Does not exist
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1 votes
2 answers
180
TIFR-2011-Maths-A-2
$\lim_{x \rightarrow 0} \sin \left(1/x^{2}\right)$ equals. $1$ $0$ $\infty$ Oscillates
$\lim_{x \rightarrow 0} \sin \left(1/x^{2}\right)$ equals.$1$$0$$\infty$Oscillates
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