If lim_(xrarr2)(f(x)-4)/(x-2)=C for constant C. Find lim_(xrarr2)f(x). What theorems were used to come to conclusion?

1 Answer
Apr 28, 2018

4

Explanation:

We can use the properties

lim_{x to a}[f(x)+g(x)] = lim_{x to a} f(x) +lim_{x to a}g(x)

and

lim_{x to a}[f(x)g(x)] = lim_{x to a} f(x) lim_{x to a}g(x)

provided both the limits on the right exists.

Thus

lim_{x to 2}(f(x)-4) = lim_{x to 2} (f(x)-4)/(x-2) lim_{x to 2}(x-2)
qquad qquad qquad qquad = C times 0 = 0

Then

lim_{x to 2}f(x) = lim_{x to 2}(f(x)-4)+lim_{x to 2}4
qquad = 0+4 = 4