Calc 2 Exam 1

Question 0

d/dx (lnx) =

Answer 0

1/x

Question 1

What is the inverse of:

Y=f(x)

Answer 1

x=f^(-1)(y)

Question 2

Integrate 1/x

Answer 2

ln(t)

Question 3

Quotient Rule:

f(x)/g(x)

Answer 3

f’(x)g(x) - g’(x)f(x)
Divided by…
[g(x)]^(2)

Question 4

e^(x+y)

Answer 4

(e^x)(e^y)

Question 5

e^(x-y)

Answer 5

(e^x)/(e^y)

Question 6

e^lnx

Answer 6

x

Question 7

ln(e^x)

Answer 7

x

Question 8

y = a^x

Answer 8

y = e^(xlna)

Question 9

Derivative of…

a^(x)

Answer 9

a^(x)lna

Question 10

log(a)x

Answer 10

lnx/lna

Question 11

Differentiate…

log(a)x

Answer 11

1/(xlna)

Question 12

limit of lnx as x glues to infinity

Answer 12

Infinity

Question 13

Limit of lnx as x approaches 0+

Answer 13

negative infinity

Question 14

Limit of e^x as x approaches infinity

Answer 14

Infinity

Question 15

Limit of e^x as x approaches (-) infinity

Answer 15

0

Question 16

Exponential function for population

Answer 16

P(t) = P(0)e^(kt)

Question 17

Money increase function

Answer 17

A(t) = A(0)(1+percent in decimal form / k)^(years x k)
K= number of months... Years... Days in a year

Question 18

Derivative of…

arccos(x)

Answer 18

(-1)/[(1-x^2)^(1/2)]

Question 19

Derivative of…

arctan(x)

Answer 19

(1)/(1+x^2)

Question 20

Derivative of…

arcsin(x)

Answer 20

(1)/[(1-x^2)^(1/2)]

Question 21

Domain of secx

Answer 21

[0,pi/2) [pi,3pi/2)

Question 22

Domain of sinx

Answer 22

(-pi/2,pi/2)

Question 23

sinh(x)

Answer 23

(e^x - e^-x)/2

Question 24

cosh(x)

Answer 24

(e^x + e^-x)/2

Question 25

e^(2x)

Answer 25

e^(x^2)

Question 26

What would you use if limit is…

0/0

Answer 26

L’Hopitals Rule

Question 27

What would you use if limit is…

infinity/infinity

Answer 27

L’Hopitals Rule

Question 28

What would you use if limit is…

0(infinity)

Answer 28

algebra

Question 29

What would you use if limit is…

infinity(infinity)

Answer 29

algebra

Question 30

What would you use if limit is…

1^(infinity)

Answer 30

ln / log

Question 31

What would you use if limit is…

0^0

Answer 31

ln / log

Question 32

What would you use if limit is…

infinity^0

Answer 32

ln / log

Question 33

Integration by parts function

Answer 33

uv - integrate(v)du

Question 34

cos^2(x) + sin^2(x)

Answer 34

1

Question 35

sin(x+y)

Answer 35

sinx cosy + cosy siny

Question 36

cos(x+y)

Answer 36

cosx cosy - sinx siny

Question 37

sin(2x)

Answer 37

2sinxcosx

Question 38

cos(2x)

Answer 38

1 - 2sin^2(x)

Question 39

cos^2(x)

Answer 39

(1 + cos2x)/2

Question 40

sin^2(x)

Answer 40

(1 - cos2x)/2

Question 41

tan^2(x) + 1

Answer 41

sec^2(x)

Question 42

Integrate secx

Answer 42

ln |secx + tanx|

Question 43

Integrate 1/(x^2 + a^2)

Answer 43

(1/a) arctan(x/a) + c

Question 44

How would you use trig substitution?

Answer 44

You would make x equal a trig value which you can switch and bring out of a square root.

Question 45

Volume of a cylinder

Answer 45

2(pi)rh(change in r)

Question 46

Cylinder method

Answer 46

Integrate from a to b

2(pi)xf(x)dx

Question 47

Work in filling water

Answer 47

Integrate distance x gravity x density x area dx

-integrating (work(force(mass(volume))))

Question 48

Arc Length

Answer 48

Integrate from a to b:
Square root (1 + [f'(x)]^2)dx

Question 49

Hooked Law

Answer 49

F = kx

Question 50

a^x

Answer 50

e^(xlna)

Question 51

loga(x)

Answer 51

lnx/lna