Is it possible to solve this limit without Hopital / Taylor / derivatives: $\lim\limits_{x \to 0} \frac{x-\sin(x)}{x^3} = \frac{1}{6}$?
100893
Determine $\lim_{x \to 0}{\frac{x-\sin{x}}{x^3}}=\frac{1}{6}$, without L'Hospital or Taylor
150981
Why doesn't using the approximation $\sin x\approx x$ near $0$ work for computing this limit?
3200
Limit of integral without Taylor expansion
117542
Finding the limit $\displaystyle\lim_{x\to 0+} \left(\frac{\sin x}x\right)^{1/{x^2}}$
70742
Evaluate $\lim_{x\rightarrow 0} \frac{\sin (6x)}{\sin(2x)}$ without L'Hopital
85531
Calculate $\lim_{x\to 0}\frac{1}{x^{\sin(x)}}$
79618
Find the limit without use of L'Hôpital or Taylor series: $\lim \limits_{x\rightarrow 0} \left(\frac{1}{x^2}-\frac{1}{\sin^2 x}\right)$
98392
Value of the limit $\lim_{x \to 0} \frac{\sin(\frac{1}{x})}{\sin(\frac{1}{x})}$
64860
Evaluation of $\lim\limits_{x\rightarrow0} \frac{\tan(x)-x}{x^3}$
125088
show that $ \lim(\sin(\frac{1}{x}))$ as $x$ approaches zero does not exist.
136810
Evaluate $\lim_{x \to 0} \frac{\sqrt{1 + \tan x} - \sqrt{1 + \sin x}}{x^3}$
122145
Evaluating Limit - $(1-(\cos x)^{\sin x})/(x^3)$
47325
Limit of quotients with square roots: $\lim_{x\to2} \frac{\sqrt{6-x}-2}{\sqrt{3-x}-1}$
64001
What is the result of $\lim\limits_{x \to 0}(1/x - 1/\sin x)$?
65239
Find $\lim_{x \to 0} \frac{x - \tan(x)}{x - \sin(x)}$
71891
$\lim_{x \to 0} f(x)=\frac{\tan 3x}{\tan 2x}$ without L'Hospital
82968
Find $(a,b)$ such that $\lim\limits_{x\to 0}\frac{f(x)}{x}=1$ implies $\lim\limits_{x\to 0}\frac{x(1+a\cos x)-b\sin x}{(f(x))^3}=1$