Determine $a, b, c$ such that $\lim_{x\to0}\frac{1}{x^5}\int_0^x{a + b\cos t+c\cos 2t}\,dt=\frac{1}{5}$
52744
The value of a, b and c for this integral
17029
How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$?
156231
Computing $\lim\limits_{n\to\infty} \int_{0}^{\infty}\frac{\sin(x/n)}{(1+x/n)^{n}}\, dx$
110126
Prove that $\lim\limits_{(x,y) \to (0,0)} \frac{{x{y^2}}}{{{x^2} + {y^4}}} = 0$
85531
Calculate $\lim_{x\to 0}\frac{1}{x^{\sin(x)}}$
122843
Finding $\int_0^\infty \frac{\cos(ax)-\cos(bx)}{x}dx$
36063
Finding the limit of $(1-\cos x)/x^2$
102408
Evaluate the limit $\lim_{x \to 0}{\frac{\sqrt{1+x\sin{x}}-\sqrt{\cos{2x}}}{\tan^{2}{\frac{x}{2}}}}$
19631
Finding $\lim_{n\to \infty}\sqrt n \int_0^1 \frac{\,dx}{(1+x^2)^n}$
76638
Find the limit $ \lim_{n \to \infty}\left(\frac{a^{1/n}+b^{1/n}+c^{1/n}}{3}\right)^n$
86634
How to find $ \lim_{(x,y)\to(0,0)} \frac{\sin^2 (x-y)}{|x|+|y|} $?
126578
Evaluate $\lim_{(x,y)\to(0,0)}\frac{\cos(xy)-1}{x^2y^2}$
36648
The limit of $((1+x)^{1/x} - e+ ex/2)/x^2$ as $x\to 0$
102425
Limit $ a_{n+1} = \frac{1}{3}(2a_n + \frac{5}{a_n^{2}}), a_1 > 0 $
32853
Computing $\lim_{A\to\infty} \frac{1}{A} \int\limits_1^A \! A^{\frac{1}{x}} \, \mathrm{d}x.$
11382
Limit $\lim\limits_{x\to0}\frac1{\ln(x+1)}-\frac1x$
20956
Correct way to prove the limit: $\mathop {\lim }\limits_{x \to 0} {x^\alpha }\int\limits_x^1 {\frac{{f\left( t \right)}}{{{t^{\alpha  + 1}}}}dt} $?