evaluate the limit

Question

if lim f(x)-2 =9

x--> 1. x-1

evaluate lim x→1 f(x).

Answer 1

The sum rule for limits states that if lim_x->1f(x) = L and lim_x->1g(x) = M, then

lim_x->1( f(x) = g(x) ) = L + M

In this example, we have f(x) and a constant. Let's say that g(x) = 2. It seems trivial, but lim_x->a2 = 2 for any real number a, including 1. So, we have the following:

lim_x->1( f(x) + g(x) ) =

lim_x->1f(x) + lim_x->1g(x) =

lim_x->1f(x) + 2 = 9

At this point, you can simply subtract 2 from each side of the equation to find the limit of f(x) as x approaches 1.