Difficult Limit Problems and Solutions

The list of tougher limit questions in calculus to learn how to use the limit rules while finding the limits of difficult functions and solutions for hard limits problems with understandable steps in different methods.

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

Evaluate $\displaystyle \large \lim_{x\,\to\,0}{\normalsize \Big(\dfrac{\sin{x}}{x}\Big)^{\dfrac{1}{x^2}}}$

Evaluate $\displaystyle \large \lim_{x\,\to\,0}{\normalsize \bigg(\dfrac{1}{x^2}-\dfrac{1}{\sin^2{x}}\bigg)}$

$\displaystyle \large \lim_{x\,\to\,0}{\normalsize \dfrac{\cos{(\sin{x})}-\cos{x}}{x^4}}$

Evaluate $\displaystyle \large \lim_{x \,\to\, a}{\normalsize \dfrac{x^x-x^a}{a^x-a^a}}$

Evaluate $\displaystyle \large \lim_{x \,\to\, 0}{\normalsize \dfrac{x+\log_{e}{\sqrt{x^2+1}-x}}{x^3}}$

Math Questions

The math problems with solutions to learn how to solve a problem.

Learn solutions

Practice now

Math Videos

The math videos tutorials with visual graphics to learn every concept.

Watch now

Subscribe us

Get the latest math updates from the Math Doubts by subscribing us.