# Prove \lim \limits_ {x \to 2} (x^4-2x^3+x+3) =5

## Question:

Prove {eq}\lim \limits_ {x \to 2} (x^4-2x^3+x+3) =5 {/eq}

## Limit:

A limit is defined as the value of a function when a variable within in the function approaches to a particular value.

The substitution method is a method to evaluate the value of the limit by directly substituting the variable with the value of the limit.

{eq}\lim_{x \rightarrow a}f(x)=f(a) {/eq}

We have to prove that

{eq}\lim \limits_ {x \to 2} (x^4-2x^3+x+3) =5 {/eq}

We evaluate the value of the limit by using the direct substitution method.

{eq}\begin{align} \lim \limits_ {x \to 2} (x^4-2x^3+x+3) &=(2)^4-2(2)^3+2+3\\ &=16-2(8)+2+3\\ &=16-16+2+3\\ &=0+5\\ &=5 \end{align} {/eq}

{eq}\color{blue}{\therefore \lim \limits_ {x \to 2} (x^4-2x^3+x+3) =5} {/eq}