I dont quite know how to solve this limit problem?

Question

They've given a graph of f and say to find the value of the left hand limit

lim (x-5) / (x-5) * f(x)
x->5-

how am i supposed to do this

Answer 1

[x→5⁻]lim (x-5)/(x-5) f(x)

First, for all x≠5, (x-5)/(x-5) f(x) = f(x), so this is:

[x→5⁻]lim f(x)

Now, if all you have is a graph of f(x), what you'll want to do is look at the value f(x) is approaching from the left. Ignore the part of the graph to the right of x=5, and ask yourself where f(x) would be if it were continuously extended from x<5. This might be the actual value of f(5) (e.g. if f is continuous), or it might be different. If it's different, there will probably be an open circle at x=5 to indicate that the function does not take on that value at x=5, in which case you'll want the y-value of the open circle that connects to a line going to the left.

Answer 2

it needs more info about f(x). This part of the limit atleast is 1