Unit 1

Question 1

1/x

Answer 1

x^-1

Question 2

1/x^p

Answer 2

x^-p

Question 3

√x

Answer 3

x^1/2

Question 4

m√x^n

Answer 4

x^n/m

Question 5

√(x^2)

Answer 5

|x|

Question 6

(√x)^2

Answer 6

x

Question 7

The instantaneous rate of change is the __________ of the function.

Answer 7

derivative

Question 8

Average rate of change of f(x) on [a,b]

Answer 8

f’(x)= (f(b) - f(a))/ b - a

Question 9

lim x->∞ (1/x)

Answer 9

0

Question 10

What does it mean when a problem states that “f(x) is differentiable?”

Answer 10

f’x exists

Question 11

ln(a*b)=

Answer 11

ln(a) + ln(b)

Question 12

ln(a/b)=

Answer 12

ln(a) - ln(b)

Question 13

lnx^p

Answer 13

plnx

Question 14

What is lim x->c- f(x)

Answer 14

The limit of f(x) as x approaches c from the left

Question 15

What is lim x->c+ f(x)

Answer 15

The limit of f(x) as x approaches from the right

Question 16

What is lim x->c f(x)

Answer 16

The limit of f(x) as x approaches from both sides

Question 17

When does the derivative of the function not exist?

Answer 17

-When the function is not continuous
-At a corner, cusp, sharp turn
-Vertical tangent line

Question 18

State the relationship between continuity and differentiability?

Answer 18

-If f(x) is continuous f(x) may or many not be differentiable
-If f(x) is differentiable f(x) is continuous

Question 19

The Intermediate Value Theorem (IVT):

Answer 19

If f(x) is continuous on [a,b], the f(a)<f(c)<f(b) for some c between a and b. (a<c<b)

Question 20

The Mean Value Theorem:

Answer 20

If f(x) is continuous and differentiable on [a,b] then f’(c)= (f(b)-f(a))/b-a. For some c between a and b.

Question 21

Equation of a tangent line

Answer 21

y-y1=m(x-x1)

Question 22

Different of a square: a^2-b^2=

Answer 22

(a+b)(a-b)

Question 23

Definition of derivative

Answer 23

f’(x)= lim h->0 f(x+h)-f(x)/h

Question 23

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