Formulas for AP Exam

Question 1

arc length of polar curve

Answer 1

integral from a to b of the square root of r^2 + (dr/d0)^2

Question 2

derivative of log{a}(x)

Answer 2

1/xln(a) ; x>0

Question 3

limit as theta approaches 0 of sin(theta)/theta

Answer 3

1

Question 4

limit as theta approaches 0 of cos(theta)-1/theta

Answer 4

1

Question 5

can limits be productized

Answer 5

yes

Question 6

can powers go outside limit

Answer 6

yes

Question 7

derivative of a^x

Answer 7

a^x * ln(a)

Question 8

difference between derivatives of arccos and arcsin

Answer 8

arccos has negative derivative

Question 9

sinx Maclaurin

Answer 9

alternating 2k+1

Question 10

limit comparison test

Answer 10

(for positive simpler terms that resemble series) take limit to infinity of quotient of two series: if has limit both converge or both diverge

Question 11

integral test

Answer 11

a(n)=f(n), if f(x) positive, cont., decreasing, then series converges or diverges with it

Question 12

root test

Answer 12

(for nth power) take limit as n to infinity of nth root of a(n). If less than one converges, more diverges

Question 13

ratio test

Answer 13

(for factorials and exponentials) take limit to infinity of n+1 term over n term. If less than 1 converges, diverges if greater

Question 14

alternating series test

Answer 14

If a(n) is decreasing, and limit to infinity is 0, then converges(abs. or cond.?)

Question 15

shell method for volume of solid of revolution

Answer 15

use for functions hard to integrate with respect to y. Volume = 2pi(int(function *x))

Question 16

washer method for volume of solid of revolution

Answer 16

pi int(r^2)

Question 17

area under polar curve

Answer 17

1/2 int r^2

Question 18

application of l’hopital

Answer 18

-+inf/-+inf 0/0

Question 19

Maclaurin for 1/1-x

Answer 19

x^n for |x|<1

Question 20

maclaurin for e^x

Answer 20

x^n/n!

Question 21

integral of tanx

Answer 21

ln|secx|+c

Question 22

integral of csc^2x

Answer 22

-cotx+c

Question 23

derivative secx

Answer 23

secxtanx

Question 24

sin2x identity

Answer 24

2sinxcosx

Question 25

integral of cscxcotx

Answer 25

-cscx

Question 26

Lagrange error bound

Answer 26

M|x-a|^n+1 / (n+1)!, M. on x to a to x to 0

Question 27

are radius' of convergence endpoints checked

Answer 27

yes

Question 28

second derivative of parametric is

Answer 28

d/dt of dy/dx over dx/dt

Question 29

tips for possible indeterminate

Answer 29

use quotients, conjugates, or ln