Math 16a worksheet 3 compute the limit limxrarr-1x2xx2-1

Question

MATH 16A WORKSHEET 3-

(1) Suppose f and g are functions that satisfy lim_x→3 f(x) = 3 and lim_x→3 g(x) = 7. Compute the following:

(a) lim_x→3(f(x)/f(x)+g(x))

(b) lim_x→3√( (f(x))² + 1)

(c) lim_x→3(f(x) + g(x))³

(d) lim_x→3 0

(2) Compute the limit lim_x→-1(x²+x/x²-1).

(3) Find a counterexample to the following statement: "We have

(lim_x→4f(x)) + (lim_x→5f(x)) = lim_x→9f(x), for any function f(x)."

(4) Let f(x) be the function defined as follows:

Draw a graph of f(x). Then compute lim _x→0f(x) and lim _x→1f(x).