# Limits Problems and Solutions

## Limit methods

#### Factorization

$(1).\,\,$ Evaluate $\displaystyle \large \lim_{x\,\to\,5}{\normalsize \dfrac{x^2-25}{x-5}}$

$(2).\,\,$ Evaluate $\displaystyle \large \lim_{x\,\to\,1}{\normalsize \dfrac{1-x^{-\dfrac{1}{3}}}{1-x^{-\dfrac{2}{3}}}}$

$(3).\,\,$ Evaluate $\displaystyle \large \lim_{x\,\to\,2}{\normalsize \dfrac{x^3+7x^2-36}{x^2+2x-8}}$

List of limits questions on factorisation to learn how to find the limit of a function by factoring.

#### Rationalization

$(1).\,\,$ Evaluate $\displaystyle \large \lim_{x\,\to\,0}{\normalsize \dfrac{\sqrt{1+x}-1}{x}}$

$(2).\,\,$ Evaluate $\displaystyle \large \lim_{x\,\to\,-1}{\normalsize \dfrac{\sqrt[\displaystyle 3]{7-x}-2}{x+1}}$

$(3).\,\,$ Evaluate $\displaystyle \large \lim_{x\,\to\,0}{\normalsize \dfrac{x}{\sqrt{a+x}-\sqrt{a-x}}}$

List of limit questions on rationalisation with solutions to learn how to find the limits by rationalization.

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### Limit of functions

#### Algebraic functions

List of limit problems with solutions for the algebraic functions to find the limits of functions in which algebraic functions are involved.

#### Trigonometric functions

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

List of limit problems with solutions for the trigonometric functions to find the limits of functions in which trigonometric functions are involved.

#### Logarithmic functions

List of limit problems with solutions for the logarithmic functions to find the limits of functions in which logarithmic functions are involved.

#### Exponential functions

List of limit problems with solutions for the exponential functions to evaluate the limits of functions in which exponential functions are involved.

### Difficult Problems

List of hard/tough problems in limits with solutions.

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