Formulas and Concepts

Question 1

If f(x) is a continuous function for all real numbers, then

Answer 1

The limit as x approaches c of f(x)= f(c)

Question 2

The limit as x approaches 0 of sinax/ax equals?

Answer 2

=1

Question 3

The limit as x approaches 0 of ax/sinax equals?

Answer 3

=1

Question 4

The limit as x approaches 1- cosax/ax equals?

Answer 4

=0

Question 5

What is l’Hopital’s Rule?

Answer 5

If the lim as x approaches c of f(x) is of the form 0/0 or ∞/∞ ; then find the lim as x approaches c for g’(x)/p’(x)

Question 6

A function f(x) is continuous at c if …

Answer 6

lim as x approaches c of f(x) exists , f(c) exists, and lim as x approaches c f(x)= f(c)

Question 7

What is the intermediate value theorem?

Answer 7

If f(x) is continuous between on the open interval [a,b], then f(x) must cross all x values in between a and b

Question 9

What is mean value theorem?

Answer 9

f’(c)= f(b) - f(a) / b-a

Question 10

The average rate of change on a function is given by the slope of the secant line…

Answer 10

m= f(b) - f(a) / b-a