Answer:
[tex]\lim_{x \to 3} f(x)=31[/tex]
Step-by-step explanation:
The function is: [tex]f(x)=x^2+8x-2[/tex], 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:
[tex]\lim_{x \to 3} f(x)=f(3)=(3)^2+8\,*\,(3)-2 =9+24-2=31[/tex]
