Unit 1: Limits and Continuity

Question 1

Define Continuity

Answer 1

A function f(x) is continuous at x=c if
1. lim (x->c) f(x) exists
2. f(c) exists
3. lim = f(c).

(limit exists, function exists, limit equals the function)

Question 2

Limit Definition of the Derivative

Answer 2

f’(x) = lim (h->0) (f(x+h)-f(x))/h

Question 3

Limit Definition of the Derivative at a point

Answer 3

f’(a) = lim (x->a) (f(x)-f(a))/(x-a)

Question 4

Average Rate of Change

Answer 4

Algebra 2 slope equation

Question 5

Calculating Differentiability

Answer 5

find limit definition from left and right
if they are equal, differentiable
if they are not equal, lim = DNE = not differentiable

Question 6

Hugely Important Idea

Answer 6

Differentiability Implies Continuity

converse of diff implies cont is not true: f(x) = |x| is continuous but not differentiable at x=0