THIS IS WHAT MATHS IS FOR ME ! JUNK OF ALPHABETS AND NUMBER

updated April 6, 2006	AP CALCULUS Stuff you MUST know Cold	* means topic only on BC
Curve sketching and analysis y = f(x) must be continuous at each: critical point: = 0 or undefined local minimum: goes (,0,+) or (,und,+) or >0 local maximum: goes (+,0,) or (+,und,) or <0 point of inflection: concavity changes goes from (+,0,), (,0,+),	Differentiation Rules Chain Rule Product Rule Quotient Rule	Approx. Methods for Integration Trapezoidal Rule Simpson’s Rule
		Theorem of the Mean Value i.e. AVERAGE VALUE
Basic Derivatives	“PLUS A CONSTANT”	If the function f(x) is continuous on [a, b] and the first derivative exists on the interval (a, b), then there exists a number x = c on (a, b) such that This value f(c) is the “average value” of the function on the interval [a, b].
	The Fundamental Theorem of Calculus
	Corollary to FTC	Solids of Revolution and friends Disk Method Washer Method General volume equation (not rotated) *Arc Length
	Intermediate Value Theorem If the function f(x) is continuous on [a, b], and y is a number between f(a) and f(b), then there exists at least one number x= c in the open interval (a, b) such that .
More Derivatives	Mean Value Theorem If the function f(x) is continuous on [a, b], AND the first derivative exists on the interval (a, b), then there is at least one number x = c in (a, b) such that .	Distance, Velocity, and Acceleration velocity = (position) acceleration = (velocity) *velocity vector = speed = * displacement = average velocity = =
	Rolle’s Theorem If the function f(x) is continuous on [a, b], AND the first derivative exists on the interval (a, b), AND f(a) = f(b), then there is at least one number x = c in (a, b) such that .

BC TOPICS and important TRIG identities and values

l’Hôpital’s Rule If , then	Slope of a Parametric equation Given a x(t) and a y(t) the slope is	Values of Trigonometric Functions for Common Angles θ sin θ cos θ tan θ 0° ,30° 37° 3/5 4/5 3/4 ,45° 53° 4/5 3/5 4/3 ,60° ,90° “ ” π,180°
Euler’s Method If given that and that the solution passes through (xo, yo), In other words:	Polar Curve For a polar curve r(θ), the AREA inside a “leaf” is where θ1 and θ2 are the “first” two times that r = 0. The SLOPE of r(θ) at a given θ is
Integration by Parts	Ratio Test The series converges if If the limit equal 1, you know nothing.	Trig Identities Double Argument
Integral of Log Use IBP and let u = ln x (Recall u=LIPET)
Taylor Series If the function f is “smooth” at x = a, then it can be approximated by the nth degree polynomial	Lagrange Error Bound If is the nth degree Taylor polynomial of f(x) about c and for all t between x and c, then	Pythagorean (others are easily derivable by dividing by sin2x or cos2x) Reciprocal Odd-Even sin(x) = sin x (odd) cos(x) = cos x (even) Some more handy INTEGRALS:
Maclaurin Series A Taylor Series about x = 0 is called Maclaurin.	Alternating Series Error Bound If is the Nth partial sum of a convergent alternating series, then Geometric Series diverges if |r|≥1; converges to if |r|<1

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