Chapter 5

Question 0

What is the definition of the natural log function

Answer 0

Lnx = integral from 1 to x of 1 over t dt, x>0

Question 1

Describe the natural logarithmic function

Answer 1

Domain (0, infinity)

Range ( -infinity, infinity )

Continuous, increasing, one to one

Concave down

Question 2

Log property

Ln(1)

Answer 2

0

Question 3

Log property

Ln(ab)

Answer 3

Ln(a) + ln(b)

Question 4

Log property

Ln(a^n)

Answer 4

n lna

Question 5

Ln (a/b)

Answer 5

Ln(a) - ln(b)

Question 6

Ln(e)

Answer 6

1

Question 7

D
— [lnx]
Dx

Answer 7

1/x , x>0

Question 8

D
— [lnu]
Dx

Answer 8

U prime
——– , u> 0
U

Question 9

What do you so when finding derivatives

Answer 9

USE ln RULES FIRST!

Question 10

Anti derivative of 1/x dx

Answer 10

Ln | x | + c

Question 11

How do you know you have to find the derivative with natural log

Answer 11

Denominator is to the power of 1

Need derivative of the denominator on top

Question 12

How do you know when it is reverse general power rule

Answer 12

Denominator is raised to power other than 1
Make it so there is no longer a denominator and then have the derivative of the quantity outside the parenthesis. Then multiply by the power, add 1 to power, put it all over new exponent

Question 13

What happens if the degree of the numerator exceeds or is equal to the degree of the denominator

Answer 13

Have to do long division

Remainder is over original denominator

Question 14

Antiderivative

Sinx dx

Answer 14

-cosx + c

Question 15

Antiderivative

tanx dx

Answer 15

• ln |cosx| + c

Question 16

Antiderivative

Secx dx

Answer 16

Ln |secx + tanx| + c

Question 17

Antiderivative

Cosx dx

Answer 17

Sinx + c

Question 18

Antiderivative

cotx dx

Answer 18

Ln | sinx | + c

Question 19

Antiderivative

Cscx dx

Answer 19

• ln | cscx + cotx | + c

Question 20

Average value

Answer 20

1 over b minus a from the integral of a to b of f of x dx

Question 21

Finding area

Answer 21

Antiderivative of function

Question 22

When are functions I verses of each other

Answer 22

When their composite function equals x

Question 23

What is the requirement of inverse functions

Answer 23

They are one to one

Must pass horizontal line test

Question 24

What are the steps to find an inverse

Answer 24

Switch x and y

Solve for y

Question 25

What are inverse functions symmetrical to

Answer 25

Origin

Question 26

Strictly monotonic

Answer 26

EITHER ALWAYS. Increasing or decreasing

Question 27

How do you know when a function is strictly monotonic

Answer 27

By attaining the derivative and seeing if it is strictly pos or neg

Question 28

When finding the inverse function always remember to…

Answer 28

State the domain and range

Question 29

Finding tangent of an inverse we can’t find

Answer 29

(F^-1) ‘ a = 1/ f’ ( f^-1(a))

Answer is the slope of the tangent of the inverse