Determine \[ \lim_{x\to -3}\frac{x^3+27}{x+3}. \]

Primary tabs

Lesson Parent: 
Function Limits V: Properties of Function Limits
Problem: 

Determine
\[
\lim_{x\to -3}\frac{x^3+27}{x+3}.
\]

Answer: 

27

SAMPLE SOLUTION

All of our problems have fully worked out, logical solutions. We connect every solution to its underlying lesson so you can understand the concepts needed to solve any problem and reinforce your learning by practicing with similar problems. All of the formulas are available to our subscribers, but here is a sample of the problem solution you will see when you log in:



Solution: 

Usually when <Sign in to see all the formulas> and <Sign in to see all the formulas> the limit <Sign in to see all the formulas> does not exist. However, if we can find an $x+3$ in the numerator to cancel the $x+3$ in the denominator the function limit might exist.

Fortunately, we know that <Sign in to see all the formulas>. This means that <Sign in to see all the formulas>. Therefore,

<Sign in to see all the formulas>

Now <Sign in to see all the formulas> is a polynomial and we know the value of function limits of polynomials. Therefore,

<Sign in to see all the formulas>