Week 4 Calculus I Outline of Notes
by
(updated
1) 2.1, Tangent and Secant lines (instantaneous, average velocity, respectively)
2) 2.2, Limit Definition
Find Limit using table of values and Graphing
Ex 1, p. 93
One-sided Limits (from Left = a-, from Right = a+), Ex1
Limit Theorem 1, pp. 98, 109
Ex 7, p 98
3) 2.2, Infinite Limits (+ = upward, - = downward)
Vertical Asymptotes, p. 100
Ex 8, p. 98; Ex 10, p.101 (use p. A27)
4) 2.3, Limit Laws, pp. 104-11,
Ex 1 (a,b,c), p. 105
Direct Substitution Property (if a in Domain of f), p.107
Ex 2b, p.106
When a NOT in domain of f (such as Domain restrictions: den 0, even root of -#),
use algebra and Limit Laws to simplify
Ex 3, p.107 (same as 2.2, Ex 1)
Ex 6, p. 108
For 2.3 HW: Read Exs 4-10 and Squeeze Thm
5) 2.4, Optional Read Proof of Limit, pp. 115-116
6) 2.5, 3 criteria for continuous:
1) a in domain of f
2) lim f exists (from left & from right same)
3) lim f(x) = f(a)
discontinuous if does NOT meet ALL 3 criteria
Ex 1, p. 124
3 types discontinuity: removable, infinite, jump; Ex 1
continuous/discontinuous from left and right, p.125; Ex 1
time permitting, Ex 2, p. 125
Read 2.5, Ex 5, p. 128 for HW