Evaluate limx→43−x+5−−−−√x−4 (proper formatting in image below) Evaluate the limit

Question

here it is

Answer 1

Let x=4+h where h is very small:

(3-√(9+h))/h=(3-√(9(1+h/9)))/h=

(3-3(1+h/9)^½)/h≃(3-3(1+h/18))/h=(3-3-h/6)/h=

-⅙.

When x=3, the expression becomes (45-24-13)/(9-5)=8/4=2. There is no anomaly because the divisor is not zero.