Evaluate the limit and explain. What is the limit at x approaches 9? Why does the limit not exist?

Question

limit as x approaches 9 at (x+5)/[(sqrt of x)-3]

Why does this limit not exist?

Answer 1

f(x) = (x + 5) / (-3 + √x)

 

Evaluate  f(8.999999) and f(9.000001).  If the limits are the same, then there is a limit.  If the limit reaches infinitely on one side and negative infinity on the other side, (or vice versa) or the limits do not equal each other, then the limit does not exist.

 

In order to be a limit as f(x) approaches x=9

 

lim f(x)    =    lim f(x)

x->9^-               x->9⁺