Question

1.f(x) = 5-x, g(x) x^3

a. lim f(x) b. lim g(x) c. lim g (f(x))
x ->1 x->4 x->-3


2. f(x) = 2x^2-3x+1, g(x) = cuberoot of x+6

a. lim f(x) b. lim g(x) c. lim g(f(x))
x->4 x->21 x->4

Answer 1

1a) Since f(x) is a polynomial (and thus is defined and has a limit for all x), simply substitute x=1.

1b) Same general comment. simply substitute x = 4.

1c) This is a composite function. Ideally, you should find the composition g(f(x)) first, and then substitute x=-3. You can do this becasuse g(f(x)) is a polynomial function.