[finding polar points]
1. find coterminal angle (r, 2n) if using tan (r, n)
for negative r: go in the opposite direction of the positive angle to find the point
for negative : go counterclockwise
[polar and rectangular conversions]
polar to rectangular co
[derivative]
substitute in r into the derivative formula
simplify and evaluate at the given angle
horizontal tangent line: top = 0 and bottom not equal to zero (dy/dt = 0 and
dx/dt is not equal to zero)
vertical tangent line/infinite slope: top not equal
[steps]
1. evaluate as normal
proper format: constant and 0 > convergeinfinity > divergestrig/ln(inf) >
DNE
improper format: indeterminate form > use a technique
note: the standard format is y = term this is useful for using logs
Use the derivative
[steps] OS of the solved for variable
1. both functions either y = f(x) or x = f(y) (choose)
2. find a and b by always going left to right for y = f(x) and bottom to top for x =
f(y) [opposite] if extra area use solution below
3. find greater function(mos
ln(x) x>0
sqrt(x) x is postive >= 0
note: negative proper fractions = 0
1 is just one of the answers of 1^infinity. the final answer is Indeterminate

both Indeterminate.
= DNE
all other trig are undefined
equals 0
equals 1
alternating
one sided limits
note: The divergence test and telescoping sums utilize the evaluation of
limts.don't confuse with the methods for sequences
for each type of series always try the divergence test first.
1. modify limit term to fit [c/infinity] in order to get a zero (get
horizontal tangent line top = 0 and bottom not equal to zero (dy/dt = 0 and
dx/dt is not equal to zero)
for ellipses a^2 >= b^2 a^2 is whichever is the larger denominator. b^2 is
whichever is the smaller denominator
the variable that the larger den is u
[fluid force on vertical surface]
1.find a and b . a is the top of the object and is labeled 0  b is the bottom of the
object [0 to .]
it is either 2 to 10 or 0 to 8 either one is correct
2. weight density[p] is 9810 for newtons and 62.4 for pounds when

Finding the interval of convergence and radius treat x as a constant when applying the
limit
1. apply the ratio test for absolute convergence then set the result < 1
if the result converges(treating x as a constant) then the interval of convergence is (
The rectangle is perpendicular to the axis of revolution (verified spring 6.3 notes)
[steps] OSO of the AOR (use if both functions opposite of aor)
1. create a mirror around the axis of revolution
2. solve both equations for x or y: [opposite] y = f(x) fo
always simplify.it is necessary to get the correct answer
[mnemonics]
differentation(powers): EVD (exponent/variable/decrease) early voting district
negative differentation: DCN (applies to cos csc and cot) disconnect [DCN on the
left side of the chart]
i