Question

Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.)

lim
x→−12

x2 + 25
− 13
x + 12

Answer 1

X approaches -12 so just plug -12 for x and solve the equation

Answer 2

there are no restrictions. all of your functions are polynomials.
2nd one is of degree 0,
3rd on is of degree 1,
and 1st one is of degree 2.

A polynomial is by definition continuous over \(\large\color{black}{ (-\infty ,+\infty) }\), and thus a limit of f(x), as x approaches any (real) number c, is going to give as the value of f(c).

and thus the conditions of continuity are met:)
lim{x-> c} f(x) = f(c)

obviously, therefore also,
lim{x->c} f(x) exists.
and
f(c) exists.