a Find the limit of the following function as x approaches t

(a) Find the limit of the following function as x approaches to 4.
y = f(x) = (x2-9x+20)/(x-4)

(b) Check whether the limit of the following function exists as x approaches to -5/3 . Is the function diferentiable at x = -5/3? Why?
y = f(x) = |3x + 5| + 6

Solution

(a) lim x-> 4 (x2-9x+20)/(x-4) => lim x-> 4 (x-5)*(x-4)/(x-4) => lim x-> 4 (x-5)= -1 (ans) (b) lim x-> -5/3 |3x + 5| + 6 = 0+6 = 6 yes the function is differentiable at x=-5/3 because the fnction is continious at that point(as it limit exists)