Prove the following statements using the precise definition

Question

1. Prove the following statements using the precise definition of the limit

a. lim_x→2 3 - 4x = - 5

b. lim_x→1 (4/3)x + 2 = 10/3.

2. Find all horizontal and vertical asymptotes of the following functions. If there are no asymptotes, say so.

a. f(x)= (x² - 4x + 3) / (6 - x - x²).

b. g(x) = e^1/x.

c. h(x)= √(x2+x+1) - √(x2+2x).