Given $\lim\limits_{x\to 0} \frac {x(1+a\cos x)-b\sin x}{x^3}=1$, what is the value of $a+b$?
82968
Find $(a,b)$ such that $\lim\limits_{x\to 0}\frac{f(x)}{x}=1$ implies $\lim\limits_{x\to 0}\frac{x(1+a\cos x)-b\sin x}{(f(x))^3}=1$
147506
Calculate $\lim\limits_{x\to4} \frac {\sqrt {1+2x}-3} {\sqrt x -2}$
145913
Find $\lim_{x\rightarrow 0} \frac{\cos x - 1}{x}$
28161
Solve $\lim_{x\to 0} \frac{\sin x-x}{x^3}$
37251
Values of the limit $\lim\limits_{x\to+\infty}\left(\sqrt{(x+a)(x+b)}-x\right)$
19056
Find the limit of $(2\sin x-\sin 2x)/(x-\sin x)$ as $x\to 0$ without L'Hôpital's rule
122093
Limit involving cosine function
50300
How to solve this limit: $\lim\limits_{x\to0}\frac{(1+x)^{1/x}-e}x$?
40487
Given $\lim_{x \rightarrow a}f(x)+\frac1{\left|f(x)\right|}=0$, what is $\lim_{x \rightarrow a}f(x)$?
27423
Why does $\lim_{x\to 0^+} x^{\sin x}=1$?
49094
Limit evaluate $\lim_{x\to0}{{\frac{\ln(\cos(4x))}{\ln(\cos(3x))}}}$?
41659
Limit as $x\to 0$ of $x\sin(1/x)$
33372
What is $\lim_{x\to\infty}\left(\sin{\frac 1x}+\cos{\frac 1x}\right)^x$?
139386
Limits of trigonometric functions: $\lim _{x\to \pi } \frac{\cos(x/2)}{\pi ^2-x^2}$
88432
A problem on range of a trigonometric function: what is the range of $\frac{\sqrt{3}\sin x}{2+\cos x}$?
135565
Limit of $\frac{1}{x^2}-\frac{1}{\sin^2(x)}$ as $x$ approaches $0$
51231
Find the limit of $\frac{n^{x}}{(1 + x)^{n}}$