Textbook Problem

Make a rough sketch of the curve y = xⁿ (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) $\underset{x\to 0^{+}}{\lim }{x}^n$

(b) $\underset{x\to 0^{-}}{\lim }{x}^n$

(c) $\underset{x\to \infty }{\lim }{x}^n$

(d) $\underset{x\to -\infty }{\lim }{x}^n$