MIdterm Hell

Question 1

What if sin is to an odd power?

Answer 1

u = cosx
1 - sin^2(x)

Question 2

What if cos is to an odd power?

Answer 2

u = sinx
cos^2(x) = 1 - sin^2(x)

Question 3

sinAcosB

Answer 3

1/2[sin(A - B) + sin(A + B)]

Question 4

cosAcosB

Answer 4

1/2[(cos(A - B) + cos(A + B)]

Question 5

sinAsinB

Answer 5

1/2[cos(A - B) - cos(A + B)]

Question 6

What if sec is to an even power?

Answer 6

u = tanx
sec^2(x) = (1 + tan^2(x))

Question 7

What if tan is to an odd power?

Answer 7

u = secx
tan^2(x) = (sec^2(x) - 1)

Question 8

root(a^2 - x^2)

a^2 - x^2

Answer 8

asinθ

Question 9

root(a^2 + x^2)

Answer 9

atanθ

Question 10

root(x^2 - a^2)

Answer 10

asecθ

Question 11

Midpoint formula?

Answer 11

△x[f(x1) + f(x2+ + f(x3) + f(x4) + f(x5)] where

Question 12

absolute error formula?

Answer 12

|A - app|

Question 13

Relative error formula?

Answer 13

|A - app|/A

Question 14

Percentage error formula?

Answer 14

(|A - appr|/A) times 100

Question 15

Trapezoid formula?

Answer 15

△x/2[f(x1) + 2f(x2) + 2f(x3) + 2f(x4) + 2f(x5) + f(x6)]

Question 16

Simpsons formula?

Answer 16

△x/3[f(x1) + 4f(x2) + 2f(x3) + 4f(x4) + 2f(x5) + f(x6)]

Question 17

Unlimited Growth

Answer 17

P(t) = Poe^kt

Question 18

Limited Growth

Answer 18

PoM/Po+(M-Po)e^-kt

Question 19

Newtons law of cooling

Answer 19

dT/dt = k(T - Ta)

Question 20

Population Growth

Answer 20

dP/dt = KP

Question 21

Motion of a Spring

Question 22

Sin^2(x) + cos^2(x) =?

Answer 22

1

Question 23

1 + tan^2(x) =?

Answer 23

sec^2(x)

Question 24

Sin(2x) =?

Answer 24

2sin(x)cos(x)

Question 25

1 + cot^2(x) =?

Answer 25

csc^2(x)

Question 26

Cos(2x) =?

Answer 26

2cos^2(x) - 1

Question 27

Derivative of sinx?

Answer 27

cosx

Question 28

Derivative of cosx?

Answer 28

-sinx

Question 29

Derivative of tanx?

Answer 29

sec^2(x)

Question 30

Derivative of secx?

Answer 30

secxtanx

Question 31

derivitive of cscx?

Answer 31

-Cscxcotx

Question 32

Antiderivitive of cosx?

Answer 32

Sin(x) + C

Question 33

derivitive of cotx?

Answer 33

-csc^2(x)

Question 34

Antiderivitive of sinx?

Answer 34

-Cosx + C

Question 35

Antiderivitive of tanx?

Answer 35

Ln|secx| + c

Question 36

Antiderivitive of secx?

Answer 36

Ln|secx + tanx| + c

Question 37

Antiderivitive of cscx?

Answer 37

-Ln|cscx + cotx| + C

Question 38

Antiderivitive of cot?

Answer 38

Ln|sinx| + c

Question 39

Antiderivitive of sec^2(x)

Answer 39

Tanx + C

Question 40

Antiderivitive of csc^2(x)

Answer 40

-cotx

Question 41

Antiderivitive of secxtanx

Answer 41

secx

Question 42

Antiderivitive of cscxcotx

Answer 42

-Csc(x)