Math Doubts

Trigonometric Limits Problems and Solutions

The limits problems are often appeared with trigonometric functions. To find limits of functions in which trigonometric functions are involved, you must learn both trigonometric identities and limits of trigonometric functions formulas. Here is the list of solved easy to difficult trigonometric limits problems with step by step solutions in different methods for evaluating trigonometric limits in calculus.

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 $\displaystyle \large \lim_{x \,\to\, 0}{\normalsize \dfrac{x-\sin{x}}{x^3}}$

Evaluate $\displaystyle \large \lim_{x \,\to\, \pi}{\normalsize \dfrac{x-\pi}{\sin{x}}}$

Find $\large \displaystyle \lim_{x \,\to\, 0}{\normalsize \dfrac{\sin{(\pi\cos^2{x})}}{x^2}}$

Evaluate $\displaystyle \lim_{x \,\to\, 0}{\dfrac{\sin{2x}+3x}{4x+\sin{6x}}}$

$\displaystyle \large \lim_{x \,\to\, \tan^{-1}{3}} \normalsize {\dfrac{\tan^2{x}-2\tan{x}-3}{\tan^2{x}-4\tan{x}+3}}$

$\displaystyle \large \lim_{x \,\to\, 0} \normalsize \dfrac{1-\cos{6x}}{1-\cos{7x}}$

$\displaystyle \large \lim_{x \,\to\, 0}{\normalsize \dfrac{x^3\sin{x}}{{(\sec{x}-\cos{x})}^2}}$

$\displaystyle \large \lim_{x \,\to\, 1}{\normalsize \dfrac{3\sin{\pi x}-\sin{3\pi x}}{{(x-1)}^3}}$

$\displaystyle \large \lim_{x \,\to\, \pi} \, \normalsize \dfrac{1-\cos{7(x-\pi)}}{5{(x-\pi)}^2}$

$\displaystyle \large \lim_{x \,\to\, 0} \normalsize \dfrac{1-\sqrt{1-\tan x}}{\sin x}$

$\displaystyle \large \lim_{x \,\to\, 0}{\normalsize \dfrac{2\sin{x}-\sin{2x}}{x^3}}$

$\displaystyle \large \lim_{x \,\to\, a}{\normalsize \dfrac{\cos{\sqrt{x}}-\cos{\sqrt{a}}}{x-a}}$

$\displaystyle \large \lim_{x \,\to\, 1}{\normalsize \dfrac{\sin{(x-1)}}{x^2-1}}$

$\displaystyle \large \lim_{x \,\to\, 0}{\normalsize \dfrac{1-\cos{x}\sqrt{\cos{2x}}}{x^2}}$

$\displaystyle \large \lim_{x \,\to\, 0}{\normalsize \dfrac{\cos{3x}-\cos{4x}}{x\sin{2x}}}$

$\displaystyle \large \lim_{\theta \,\to\, 0}{\normalsize \dfrac{\sin{5\theta}-\sin{3\theta}}{\theta}}$



Math Doubts
Math Doubts is a best place to learn mathematics and from basics to advanced scientific level for students, teachers and researchers. Know more
Follow us on Social Media
Mobile App for Android users Math Doubts Android App
Math Problems

Learn how to solve easy to difficult mathematics problems of all topics in various methods with step by step process and also maths questions for practising.

Learn more