The limits problems involving the trigonometric functions appear in calculus. So, the limits of trigonometric functions worksheet is given here for you and it consists of simple to tough trigonometric limits examples with answers for your practice, and also solutions to learn how to find the limits of trigonometric functions in possible different methods by the trigonometric limits formulas.
Evaluate $\displaystyle \large \lim_{x\,\to\,0}{\normalsize \Big(\dfrac{\sin{x}}{x}\Big)^{\dfrac{1}{x^2}}}$
Evaluate $\displaystyle \large \lim_{x\,\to\,0}{\normalsize \dfrac{1-\cos{mx}}{1-\cos{nx}}}$
Evaluate $\displaystyle \large \lim_{x\,\to\,0}{\normalsize \dfrac{\log_{\displaystyle e}{\big(\cos{(\sin{x})}\big)}}{x^2}}$
Evaluate $\displaystyle \large \lim_{x\,\to\,\Large \frac{\pi}{4}}{\normalsize \dfrac{\sin{x}-\cos{x}}{x-\dfrac{\pi}{4}}}$
Evaluate $\displaystyle \large \lim_{x\,\to\,0}{\normalsize \dfrac{\sin^3{x}}{\sin{x}-\tan{x}}}$
Evaluate $\displaystyle \large \lim_{x\,\to\,0}{\normalsize \dfrac{\log_{e}{(\cos{x})}}{\sqrt[\Large 4]{1+x^2}-1}}$
Evaluate $\displaystyle \large \lim_{x \,\to\, 0}{\normalsize \dfrac{e^x-e^{x\cos{x}}}{x+\sin{x}}}$
Evaluate $\displaystyle \large \lim_{x\,\to\,0}{\normalsize \dfrac{1-\cos{(2x)}}{x^2}}$
Evaluate $\displaystyle \large \lim_{x \,\to\, 0}{\normalsize \Big(1+\sin{x}\Big)^{\Large \frac{1}{x}}}$
Evaluate $\displaystyle \large \lim_{x \,\to\, 0}{\normalsize \dfrac{(e^{-3x+2}-e^2)\sin{\pi x}}{4x^2}}$
Evaluate $\displaystyle \large \lim_{x \,\to\, 2}{\normalsize \dfrac{\cos{\Big(\dfrac{\pi}{x}\Big)}}{x-2}}$
Evaluate $\displaystyle \large \lim_{x \,\to\, 0}{\normalsize \dfrac{x\tan{2x}-2x\tan{x}}{(1-\cos{2x})^2}}$
Evaluate $\displaystyle \large \lim_{x \,\to\, \frac{\pi}{2}}{\normalsize \dfrac{\cos{x}}{\frac{\pi}{2}-x}}$
Evaluate $\displaystyle \large \lim_{x \,\to\, \pi}{\normalsize \dfrac{\sqrt{2+\cos{x}}-1}{(\pi-x)^2}}$
Evaluate $\displaystyle \large \lim_{x \,\to\, 0}{\normalsize \dfrac{\tan{x}-\sin{x}}{x^3}}$
Evaluate $\displaystyle \large \lim_{x \,\to\, 0}{\normalsize \dfrac{(1-\cos{2x})(3+\cos{x})}{x\tan{4x}}}$
Evaluate $\displaystyle \large \lim_{x \,\to\, \frac{\pi}{2}}{\normalsize \dfrac{1+\cos{2x}}{(\pi-2x)^2}}$
Evaluate $\displaystyle \large \lim_{x \,\to\, 0}{\normalsize \sqrt[x^3]{1-x+\sin{x}}}$
Evaluate $\displaystyle \large \lim_{x \,\to\, 0}{\normalsize \dfrac{\sin{3x}}{\sin{4x}}}$
Evaluate $\displaystyle \large \lim_{x \,\to\, \pi}{\normalsize \dfrac{x-\pi}{\sin{x}}}$
Evaluate $\displaystyle \large \lim_{x \,\to\, 0}{\normalsize \dfrac{x-\sin{x}}{x^3}}$
Find $\large \displaystyle \lim_{x \,\to\, 0}{\normalsize \dfrac{\sin{(\pi\cos^2{x})}}{x^2}}$
Evaluate $\displaystyle \lim_{x \,\to\, 0}{\dfrac{\sin{2x}+3x}{4x+\sin{6x}}}$
$\displaystyle \large \lim_{x \,\to\, \tan^{-1}{3}} \normalsize {\dfrac{\tan^2{x}-2\tan{x}-3}{\tan^2{x}-4\tan{x}+3}}$
$\displaystyle \large \lim_{x \,\to\, 0} \normalsize \dfrac{1-\cos{6x}}{1-\cos{7x}}$
$\displaystyle \large \lim_{x \,\to\, 0}{\normalsize \dfrac{x^3\sin{x}}{{(\sec{x}-\cos{x})}^2}}$
$\displaystyle \large \lim_{x \,\to\, 1}{\normalsize \dfrac{3\sin{\pi x}-\sin{3\pi x}}{{(x-1)}^3}}$
$\displaystyle \large \lim_{x \,\to\, \pi} \, \normalsize \dfrac{1-\cos{7(x-\pi)}}{5{(x-\pi)}^2}$
$\displaystyle \large \lim_{x \,\to\, 0} \normalsize \dfrac{1-\sqrt{1-\tan x}}{\sin x}$
$\displaystyle \large \lim_{x \,\to\, 0}{\normalsize \dfrac{2\sin{x}-\sin{2x}}{x^3}}$
$\displaystyle \large \lim_{x \,\to\, a}{\normalsize \dfrac{\cos{\sqrt{x}}-\cos{\sqrt{a}}}{x-a}}$
$\displaystyle \large \lim_{x \,\to\, 1}{\normalsize \dfrac{\sin{(x-1)}}{x^2-1}}$
$\displaystyle \large \lim_{x \,\to\, 0}{\normalsize \dfrac{1-\cos{x}\sqrt{\cos{2x}}}{x^2}}$
$\displaystyle \large \lim_{x \,\to\, 0}{\normalsize \dfrac{\cos{3x}-\cos{4x}}{x\sin{2x}}}$
$\displaystyle \large \lim_{\theta \,\to\, 0}{\normalsize \dfrac{\sin{5\theta}-\sin{3\theta}}{\theta}}$
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