Register

Recent questions tagged limits

2 2 votes
1 answers 1 answer
1.1k
1.1k views
Limit
Puzzle$\lim_{y\rightarrow \alpha }\left (y-\left ( y^{2}+y \right )^{\frac{1}{2}}\right )$
User Avatar
0 0 votes
0 0 answers
710
710 views
Limits
$\displaystyle\lim_{x \to 0} \left[ \dfrac{log(1+x)}{x} \right] ^{\dfrac{1}{x}} $
User Avatar
4 4 votes
2 answers 2 answers
1.8k
1.8k views
Limit
Is answer will be 1 or 5?$\lim_{x\rightarrow \alpha }\left ( \frac{x+6}{x+1} \right )^{x+4}$
User Avatar
0 0 votes
1 1 answer
906
906 views
ISI-2016-05
Let $$f(x,y) = \begin{cases} \dfrac{x^2y}{x^4+y^2}, & \text{ if } (x,y) \neq (0,0) \\ 0 & \text{ if } (x,y) = (0,0)\end{cases}$$Then $\displaystyle{\lim_{(x,y)...
User Avatar
5 5 votes
2 answers 2 answers
2.1k
2.1k views
ISI2017-MMA-14
Let $(v_n)$ be a sequence defined by $v_1 = 1$ and $v_{n+1} = \sqrt{v_n^2 +\left(\dfrac{1}{5}\right)^n}$ for $n\geq1$. Then $\displaystyle{\lim_{n \rightarrow \infty}v_n}...
User Avatar
1 1 vote
1 1 answer
1.9k
1.9k views
ISI-2014
Consider the function for all $x \in (0,1),$$\begin{equation}f(x) =\begin{cases}x &\text{if x is rational}\\1-x & \text{otherwise.}\end{cases} \end{equation}$Then, the fu...
User Avatar
2 2 votes
1 answers 1 answer
1.3k
1.3k views
Mathematics GATE 2018 CH: 33
If $y = e^{-x^2}$ then the value of $\displaystyle\lim_{x \to \infty} \dfrac{1}{x}\dfrac{\mathrm{d}y}{\mathrm{d}x}$ is _________ .
User Avatar
1 1 vote
0 0 answers
2.5k
2.5k views
Limits
Is there any other way instead of using general formula for sum of "to the 4" of first n natural numbers
User Avatar
2 2 votes
1 answers 1 answer
1.9k
1.9k views
Calculus Limit
Find the value of Here I got till $lim_{x \rightarrow \infty} \frac{4^2 + \frac{3^x}{4^x}}{4^{-2}}$. But how to proceed further?
User Avatar
6 6 votes
1 answers 1 answer
1.4k
1.4k views
MadeEasy Test Series 2018: Calculus - Limits
The value of $\lim_{x\rightarrow \infty }\left ( \frac{4^{x+2} + 3^{x}}{4^{x-2}} \right )$ is ____________
User Avatar
2 2 votes
1 1 answer
1.3k
1.3k views
Limits
Find the value of above limit.How to approach with this type of infinity power infinity problems ??im thinking like first we should convert this to 1 power infinity prob...
User Avatar
4 4 votes
1 1 answer
1.2k
1.2k views
Limits
User Avatar
3 3 votes
1 answers 1 answer
1.3k
1.3k views
Calculus (LIMITS)
Answer is 1. I also know the procedure. My question is why isn't this formula working?Am I doing something wrong?
User Avatar
4 4 votes
0 0 answers
1.1k
1.1k views
Limits
What is the value of $\displaystyle \lim_{x\to \infty} \left(\frac{x}{2+x}\right)^{2x}?$
User Avatar
3 3 votes
2 2 answers
1.6k
1.6k views
Continuity and Differentiability of root mod function
1) Consider f(x) = $|x|^{3/2}$ Check for Differentiability and Continuity. I am getting Cont and Differentiable both.2) Consider f(x) = $|x-1|^{3/2}$ Check for Differen...
User Avatar
6 6 votes
1 answers 1 answer
8.4k
8.4k views
Limit and Continuity
Evaluate the given limit :$lim_{x\rightarrow0} \ {\Large \frac{(1+x)^{\frac{1}{x}}-e}{x}}$options :$ \\ a) \frac{e}{8} \\ b) -\frac{e}{2} \\ c)- \frac{e}{4} \\ d) 1$
User Avatar
2 2 votes
2 2 answers
1.9k
1.9k views
MadeEasy Test Series: Calculus - Limits
How it solve this ?
User Avatar
1 1 vote
0 0 answers
2.6k
2.6k views
limit question find answer
$\lim_{x\rightarrow\infty}(\sqrt{x}-x)=?$
User Avatar
0 0 votes
1 1 answer
2.2k
2.2k views
Limit question
$\lim_{x\rightarrow0}\frac{x^{2}+1}{x(x-1)}=?$
User Avatar
0 0 votes
0 0 answers
696
696 views
Limit exists- L'Hospital Rule
Consider we have a limit of the form $\dfrac{0}{0}\ or\ \dfrac{\infty}{\infty} $ and we need to find the value of the limit. Since we have an indeterminate form should we...
User Avatar
3 3 votes
1 answers 1 answer
2.9k
2.9k views
Limit
the value of :-$\lim_{x \rightarrow 0}(\frac{1}{x^2} - \frac{1}{sin^2x})$Is_______Answer given is -1\3
User Avatar
1 1 vote
2 answers 2 answers
723
723 views
virtual-gate
User Avatar
1 1 vote
2 answers 2 answers
719
719 views
virtual gate
User Avatar
3 3 votes
2 answers 2 answers
1.5k
1.5k views
EM: Limits
Please solve the following question:
User Avatar
0 0 votes
1 answers 1 answer
986
986 views
limit
solve following $\lim_{x->0} e^{ax}- e^{-ax}/ log(1+bx)$
User Avatar
4 4 votes
5 5 answers
1.4k
1.4k views
calculus problem on limits
User Avatar
1 1 vote
1 1 answer
1.2k
1.2k views
calculus problem on limits
1)2)Answer for 1) infinity 2) 1/sqrt(3)please verify
User Avatar
1 1 vote
0 0 answers
917
917 views
limit
User Avatar
1 1 vote
1 1 answer
1.0k
1.0k views
Proof Results in Limits
Proof these results in limits1. $\lim_{x\rightarrow0}(1+x)^{1/x} = e$2. $\lim_{x\rightarrow0}(1+nx)^{1/x} = e^n$3. $\lim_{x\rightarrow\infty }(1+\frac{1}{x})^{x} = e$4. $...
User Avatar
1 1 vote
1 1 answer
500
500 views
Doubt in calculus
How to solve question 1 without reduction formula.Q1 $\int_{0}^{ \Pi /2}sin^6xcos^2xdx$Q2 $\lim_{x\rightarrow0}\frac{1-cos^2}{2x^4}$
User Avatar
Page: