Question

Find the limit of the function by using direct substitution. (2 points) limit as x approaches three of quantity x squared plus eight x minus two.

Answer 1

`\lim_(x \to 3) f(x)=31`

Explanation:

The function is:
`f(x)=x^2+8x-2`, and we need to find the limit when x approaches 3 of it by what is called direct substitution. This method can be used as long as the function is not undefined at the point in question.

In this case, as the function is a polynomial, it is well defined for all real numbers, and the limit can be evaluated just by substituting the value x with the number "3" one wants to approach:

`\lim_(x \to 3) f(x)=f(3)=(3)^2+8\,*\,(3)-2 =9+24-2=31`