## Lecture Notes: Monday, September 14, 1998

#### Limits and One-sided Limits

- x^2 as x -> 0.
- sin(1/x) as x -> 0.
- Modify MAPLE Demo # 1 to help here and on other examples as
well.

- y = x, x not 0, y = 1 for x = 0 as x -> 0.
- 1/x as x -> 0
- limit of arctan(x) as x goes to +infinity and -infinity
- more on one-sided limits
- precise definition of limit

**indeterminate forms:**

- (x^2 - 9)/(x-3) as x -> 0.
- sin(4*x)/3*x as x -> 0. Use MAPLE Demo #1 to help.
- sqrt(x+1) - sqrt(x) as x -> plus infinity. Rationalize.
Also use Demo #1.
- (3*x^2 + 2*x - 1)/(x^2 - 8*x) as x -> plus infinity.
Calculate, use Demo #1, plot
- Note horizontal asymptote.