Exam 2

Question 1

Indeterminate forms you can use L’Hospital’s Rule on

Answer 1

0/0, ∞/∞, ∞/-∞, -∞/-∞

Question 2

0 * ∞ or 0 * -∞

Answer 2

rewrite as g(x)(1/f(x)) or f(x)/(1/g(x)) to get into form you can use L’Hospital’s Rule on

Question 3

∞-∞

Answer 3

Use algebra (common denominators) to rewrite in a form you can use L’Hospital’s Rule on

Question 4

0^0, ∞^0, or 1^∞

Answer 4

Use natural logarithms to rewrite in a form you can use L’Hospital’s Rule with. Let y=the indeterminate form–>take limit of both sides. —> Don’t forget to relate y back to the original limit

Question 5

Product Rule in limit

Answer 5

Integration by parts

Question 6

Integration by parts formula

Answer 6

the integral of (udv) = uv - the integral of (vdu)

Question 7

What to let u equal when using integration by parts

Answer 7

LIPET
Logarithm, Inverse trig function, Polynomial, Exponential, Trig function

Question 8

Trigonometric integrals - cosine and sine

Answer 8

cosine squared + sine squared = 1

Question 9

Trigonometric integrals - tangent and secant

Answer 9

1 + tangent squared = secant squared

Question 10

Trigonometric integrals - cotangent and cosecant

Answer 10

1 + cotangent squared = cosecant squared

Question 11

Half angle formula - cosine

Answer 11

cosine squared = 0.5(1+cosine(2x))

Question 12

Half angle formula - sine

Answer 12

sine squared = 0.5(1-cosine(2x))

Question 13

Double angle formula

Answer 13

sin(2x) = 2sinxcosx

Question 14

Derivative - sine (o/h)

Answer 14

cosine

Question 15

Derivative - cosine (a/h)

Answer 15

-sin

Question 16

Derivative - tangent (o/a)

Answer 16

Secant squared

Question 17

Derivative - secant (h/a)

Answer 17

tanxsecx

Question 18

Derivative - cotangent (a/o)

Answer 18

-cosecant squared

Question 19

Derivative - cosecant (h/o)

Answer 19

-cscxcotx

Question 20

integral of secant squared

Answer 20

tanx +c

Question 21

integral of cosecant squared

Answer 21

-cotx +c

Question 22

integral of tanx

Answer 22

ln|secx| +c

Question 23

integral of secx

Answer 23

ln|secx+tanx| +c

Question 24

integral of secxtanx

Answer 24

secx

Question 25

integral of cscxcotx

Answer 25

-cscx

Question 26

integral of cotx

Answer 26

ln|sinx|+c

Question 27

integral of cscx

Answer 27

ln|cscx-cotx| +c

Question 28

Trigonometric substitutions: a^2 + x^2

Answer 28

Let x=atan(theta)

Question 29

Trigonometric substitutions: a^2 - x^2

Answer 29

Let x=asin(theta)

Question 30

Trigonometric substitutions: x^2 - a^2

Answer 30

Let x=asec(theta)

Question 31

the integral of P(x)/Q(x)

Answer 31

Partial fractions

Question 32

P(x) > Q(x)

Answer 32

long division

Question 33

P(x) < Q(x)

Answer 33

Partial fractions

Question 34

Linear factors

Answer 34

single variable on top (A, B, C...)

Question 35

Irreducible Quadratic

Answer 35

Linear fuction on top (Ax+B, Cx+D...)

Question 36

the nth root (g(x))

Answer 36

Let u=the nth root(g(x)) to change integrand into rational fraction

Question 37

the integral of x^n when n does not =0

Answer 37

(x^(n+1))/(n+1)

Question 38

the integral of 1/x

Answer 38

ln|x|

Question 39

the integral of e^x

Answer 39

e^x

Question 40

the integral of b^x

Answer 40

(1/(lnb))*(b^x)