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}

Answer and Explanation:


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}


Learn more about this topic:

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How to Determine the Limits of Functions

from Math 104: Calculus

Chapter 6 / Lesson 4
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