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if slices are horizontal. Physical Applications: Physics Formulas. Associated Calculus Problems. Mass: Mass = Density * Volume (for 3-D objects).

domain of g = all real numbers. Functions which are defined by different formulas on different intervals are sometimes called piecewise defined functions.

Differentiation Formulas d dx k = 0 (1) d dx [f(x)±g(x)] = f0(x)±g0(x) (2) d dx [k ·f(x)] = k ·f0(x) (3) d dx [f(x)g(x)] = f(x)g0(x)+g(x)f0(x) (4) d dx f(x) g(x ...

CALCULUS BC ONLY Differential equation for logistic growth: , where lim t dP kP L P L P t dt of Integration by parts: ³³u dv uv vdu Length of arc for functions: 1 [ ( )] 2 b a s f x dx ³ c _____ If an object moves along a curve, its Position vector = x t y t ,

Visit http://tutorial.math.lamar.edu for a complete set of Calculus notes. ... Basic Limit Evaluations at ± ∞ ... Basic Properties and Formulas.

Fundamental Theorem of Calculus: ' x a d F xftdtfx dx where f t is a continuous function on [a, x]. b a f xdx Fb Fa, where F(x) is any antiderivative of f(x). Riemann Sums: 11 nn ii ii ca c a 111 nnn ii i i iii ab a b 1 lim ( ) b n n

Source: adapted from notes by Nancy Stephenson, presented by Joe Milliet at TCU AP Calculus Institute, July 2005 AP Calculus Formula List Math by Mr. Mueller Page 2 of 6 [ ] ( ) ( ) ( ) Intermediate Value Theorem: If is continuous on , and is any number between and ,

for all in , then the graph of is concave down on . Inflection Point: A function has an inflection point at c f c, if fcc changes sign at xc Fundamental Theorems First Fundamental Theorem of Calculus: b c³ a f x dx f b f a (The accumulated change in f from a to b) Second Fundamental Theorem of Calculus: gx c a d f t dt f g x g x dx ³ or

Differential Equations. ... Calculus of Variations. ... If n is a positive integer the series terminates and is valid for all x: the term in xr is nCrxr or ...

The right way to begin a calculus book is with calculus. This chapter will jump ... Every formula to compute v from f will have f divided by time.

Inflection Points of the PDF of the Normal Distribution. Appendices ... Inverse Trigonometric Functions (Basic Formulas).

Equation of a plane A point r (x, y, z)is on a plane if either (a) r bd= jdj, where d is the normal from the origin to the plane, or (b) x X + y Y + z Z = 1 where X,Y, Z are the intercepts on the axes. Vector product A B = n jAjjBjsin , where is the angle between the vectors and n is a unit vector normal to the plane containing A and B in the direction for which A, B, n form a right-handed set ...

Calculus Formulas _____ The information for this handout was compiled from the following sources:

1. Polynomials for all x. 2. Rational function, except for x’s that give division by zero. 3. n x (n odd) for all x. 4. n x (n even) for all x 0. 5. ex for all x. 6. ln x for x 0. 7. cos x and sin x for all x. 8. tan x and sec x provided 33,,,,, 2222 x 9. cot x and csc x provided

Understanding Calculus: Problems, Solutions, and Tips Scope: The goal of this course is for you to understand and appreciate the beautiful subject of calculus. You will see how calculus plays a fundamental role in all of science and engineering, as well as business and economics.

that is continuous on a closed interval (a,btakes on every value ... Solving Differential Equations: Graphically and Numerically. Slope Fields. At every ...

Created Date: 3/16/2008 2:13:01 PM

Created Date: 3/16/2008 2:13:01 PM

Differentiation Formulas d dx k = 0. (1) d dx. [f(x) ± g(x)] = f (x) ± g (x) ... Integration Formulas. ∫ dx = x + C. (1). ∫ xn dx = xn+1.

AP Calculus Formula List Math by Mr. Mueller Page 6 of 6 ( ) ( ) ( ) ( ) ( ) 2 2 2 Polar Coordinates and Graphs: For : cos , sin , , tan cos ' sin cos 'sin Slope of a polar curve: sin ' cos sin 'cos Area inside a polar curve y r f x r y r r x y x dy dy d r rf f dx dx d f f r r

Exercises and Problems in Calculus John M. Erdman Portland State University Version August 1, 2013 c 2010 John M. Erdman E-mail address: erdman@pdx.edu

AP CALCULUS AB & BC FORMULA LIST ... Let f be a function such that the second derivative of f exists on an open interval containing c. 1) If fcc 0 0 and fccc !, then is a relative minimum. ... for all x in I, then the graph of f is concave upward in I. 2) If

So, Binils.com comes with the Maths notes solution to the students with a complete Calculus formula sheet pdf file. This Maths formulae pdf ...

1. Polynomials for all x. 2. Rational function, except for x’s that give division by zero. 3. n x (n odd) for all x. 4. n x (n even) for all x 0. 5. ex for all x. 6. ln x for x 0. 7. cos x and sin x for all x. 8. tan x and sec x provided 33,,,,, 2222 x 9. cot x and csc x provided

Integral Calculus Formula Sheet Derivative Rules: 0 d c dx nn 1 d xnx dx sin cos d x x dx sec sec tan d x xx dx tan sec2 d x x dx cos sin d x x dx csc csc cot d x xx dx cot csc2 d x x dx d aaaxxln dx d eex x dx dd cf x c f x dx dx

Calculus Summary Formulas. Differentiation Formulas ... takes on every value between . )( xfy. = and )( f a. ] ba,. )(b f. Note: If is continuous on [.

Calculus Formulas _____ The information for this handout was compiled from the following sources: ... If f "(x) >0 for all x in an interval I ther f (x) is concave up ...