Unit 3

Question 1

How do we write “as x gets closer and closer to a but does not become a”

Answer 1

X-> a

Question 2

What are the steps in finding a limit?

Answer 2

1. Direct substitution, if that is indeterminate, go to 2

2. Tweak expression to avoid indeterminate (factor etc)

Question 3

What is the formula for limits at infinity?

Answer 3

Lim (1/(x^n))= 0

X->infinity

Question 4

What is infinity multiplied by x?

What is 1 divided by infinity?

Answer 4

A) Infinity

B) 0

Question 5

What is the definition of a square root x^2?

Answer 5

Square root (x^2) = |x| { x, if x > or equal to 0
-x, if x< o}

Question 6

What are the three rules to see if there is continuity at point x=c?

Answer 6

1. f(c) is defined
2. Lim f(x) exists
   X->c
3. Lim f(x) = f(c)
   X->c

Question 7

What is right continuous?

At x=a

Answer 7

Lim f(x) = f(a)
X->a+

Question 8

What is left continuous?

At x=b

Answer 8

Lim f(x) = f(b)
X->b-

Question 9

What is the intermediate value theorem?

Answer 9

States that if a function y=f(x) is continuous on the closed interval a

Question 10

What is the formula for the average rate of change? What slope is this?

Answer 10

f(b) - f(a) / b-a

Two points (a, f(a)) and (b, f(b))

Slope of the secant line joining these two points

Or y2-y1 / x2-x1

Question 11

What is instantaneous rate of change? What’s are the two formulas?

Answer 11

The slope of the tangent line at x=a

Lim (f(a+h)-f(a)) / h
H->0

Use this one!! V
Lim (f(c)-f(a)) / x-a
x->a

Question 12

What is velocity?

Answer 12

Instantaneous rate of change of the displacement

Question 13

What is the complex equation of the derivative? What is the alternate form?

Answer 13

Lim f(x+h)-f(x) / h
h->0
Alternate:

Lim f(b)-f(x) / b-x
b->x

Question 14

What are the three scenarios where the derivative does not exist?

Answer 14

1. F is discontinuous
2. f has a sharp corner
3. f has a vertical tangent line