GRE Math Subject test

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Derivative of tan(x)
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Try to break up the absolute value if the limit is approaching from a certain direction
Find the derivative to get tangent slope, then take inverse reciprocal for normal slope
Volume of a sphereIntegral of a^xIntegral of sec^2(x)Integral of csc^2(x)Integral of sec(x)tan(x)Integral of csc(x)cot(x)Integral of 1/(1-x^2)^.5arcsin(x)Integral of 1/(1+x^2)arctan(x)Trigonometric Substitution for sqrt(a^2-x^2)x=asin(u)Trigonometric Substitution for sqrt(a^2+x^2)x=atan(u)Trigonometric Substitution for sqrt(x^2-a^2)x=asec(u)When can you use partial fractions?If the degree of the denominator is greater than the numeratorWhat do you do if there are terms in partial fractions with order higher than one?You make n fractions where the nth fraction has the nth orderThe sum of k^2 from 0 to nn(n+1)(2n+1)/6The mean value TheoremThe equation of a cardioidr=2a(1+cos(theta))Area in polar coordinatesVolume by revolution around the x-axisVolume by revolution around the y-axisWasher MethodFormula for arc lengthThe number e limite=lim n-->inf of (1+1/n)^nWhen can you use L'Hospitals rule?When the limit is indeterminate. i.e. 0/0 or inf/infWhat are the two kinds of improper integrals1st kind which means that one or both of the bounds blows up to infinity and the 2nd kind which means the integrand blows up to infinity somewhere on or within th e boundsIf both bounds of integration are infinite, you have to...split the integral into two separate integralsIf the integrand blows up to infinity somewhere in the bounds, you have to...split the integral into twoGeometric SeriesThe comparison testThe ratio testThe root testThe integral testAlternating Series TestAn alternating series converges if the an's monotonically decrease with a limit of zeroEvery absolutely convergent series is alsoconvergentHow do you find the radius of convergence?Either use the ratio or root test and find inequality for |x|Power SeriesSigma of (x^n)=1/(1-x)Taylor SeriesTaylor Series for sin(x)Taylor Series for cos(x)Taylor Series for exponential functionSigma (1/n!)*x^nTaylor Series of log(1+x)Taylor Series errorThe dot product(Both formulas)Vector Projection(b onto a)The area of a parallelogram||A x B||The volume of a parallelepiped|(A x B). C|How do you find the vector between two points?You just subtract their respective components and the result is the desired vectorParametric EquationsSymmetric Equations(a, b and c are respective x y and z vectors)The equation of a plane( where a b and c are the components of the normal vector)How do you find the equation of a plane with points A, B and C?First, you find AB and AC and take their cross product. This is now your normal vector and its gucci from hereHow do you find the equation of a cylinder along a certain vector?The vector v is used in the symmetric equations and the curve gives you a (x0,y0,z0) and relations between the variablesHow to find the surface of revolution?How do you find the level curves of a nth dimensional function?Just set the nth dimensional equal to cSpherical coordinatesHow do you find the equation of a line tangent to an intersection?Compute grad f and grad g and take cross product to find the vector v and then input into parametric equation formulaTangent plane of a surfaceSandwich TheoremInclusion-Exclusion PrincipleDefinition of a fieldDefinition of a vector spaceThe product of two cyclic groups is cyclic IFF their respective orders are caprice, aka gcd(g,f)=1How do you find expected value given a probability density function?How do you find variance given probability density function?