MTH 253 Lecture 13: 9.2 Part 2 Vectors

Make a rough sketch of the curve (n an integer) for the following five cases:

(i) n = 0 (ii) n > 0, n odd (iii) n > 0, n even (iv) n < 0, n odd (v) n < 0, n even

Then use these sketches to find the following limits.

(a) (b) (c) (d)

Sketch the graph of a function f with the following properties:

(i) f(-3) = 0, f(-1) = 3;
(ii) Asymptotes: x = 2, and y = -1;
(iii) f '(3) does not exist, f(3) = 2;
(iv) f '(x) > 0 for x < -1 and 2 < x < 3, f '(x) < 0 for -1 < x < 2 and x >3;
(v) f ''(x) > 0 for x < -3 and x > 3, f ''(x) < 0 for -3 < x < 3.