Question

Find the limit of the function algebraically. limit as x approaches negative three of quantity x squared minus nine divided by quantity x cubed plus three.

Answer 1

The limand is continuous at
`x=-3`, so you can directly substitute
`x=-3` to get


`\displaystyle\lim_(x\to-3)(x^2-9)/(x^3+3)=((-3)^2-9)/((-3)^3+3)=(9-9)/(-27+3)=0`

Did you mean to write
`x^3+3^3=x^3+27` in the denominator by any chance? In that case, you would instead have


`\displaystyle\lim_(x\to-3)(x^2-9)/(x^3+3)=\lim_(x\to-3)((x+3)(x-3))/((x+3)(x^2-3x+9))=\lim_(x\to-3)(x-3)/(x^2-3x+9)=(-3-3)/((-3)^2-3(-3)+9)=-\frac29`