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$integration of rational functions by partial fraction decomposition & rationalizing substitution$

polar curves: symmetry tests and graphing circles & limacons

math with yosh

math with yosh

polar curves: symmetry tests and graphing circles & limacons

polar coordinates

x & y-intercepts, slope, eqns in point-slope & slope-intercept form, parallel & perpendicular lines

graphing rational functions

solving systems of two and three variables by graphing, substitution, and elimination

law of cosines

frq: ap calculus bc exam 2007 #3 polar equations

frq: ap calculus bc exam 2014 #4 polar equations

frq: ap calculus bc exam 2009 (form b) #4 polar equations

areas and lengths in polar coordinates

polar coordinates and curves: first derivative, circles, rose curves, limacons, and lemniscates

vectors / particle motion: magnitude, position, velocity, acceleration, speed, and distance traveled

parametric curves: 1st and 2nd derivatives, applications, and arc length

curves defined as parametric equations

taylor polynomials and taylor's inequality / lagrange error bound

taylor and maclaurin series

representations of functions as power series: part two

representations of functions as power series

power series

strategy for testing series

alternating series test and alternating series error bound theorem

absolute convergence and the ratio and root tests

the comparison test & the limit comparison test

integral test, p-series, and remainder estimate of sums

infinite series

sequences

models for population growth - logistic growth, logistic differential equations, & carrying capacity

models for population growth - exponential growth & decay

separable equations

euler's method

slope fields and differential equations

improper integrals

integration strategy and integration formulas

integration of rational functions by p.f.d., u-substitution, completing the square, & arctanx

integration of rational functions by partial fraction decomposition & rationalizing substitution

trigonometric integrals

integration by parts

volumes of known cross sections

volume of rotation: disk method about the x/y-axis (part two)

arc length

particle motion revisited

the definite integral as an accumulation function

average value of a function

areas between curves

the substitution rule with definite integrals

the substitution rule with indefinite integrals

indefinite integrals: part two

SOLVING RATIONAL EQUATIONS

riemann sums

antiderivatives

optimization

summary of curve sketching

l'hopitals rule and indeterminate forms

increasing/decreasing, maximums/minimums, concavity, inflection points, & 1st/2nd derivative tests

rolle's theorem & the mean value theorem

local & absolute maximum & minimum values & critical numbers

linear approximation

related rates

applications of the derivative

derivatives of log functions & logarithmic differentiation

derivatives of inverse functions

implicit differentiation

the chain rule

derivatives of trig functions

the product and quotient rules

derivatives of polynomials and exponential functions (using differentiation formulas)

derivative as a function and graphing derivatives

derivatives and rates of change: part two

derivatives and rates of change: part one

continuity & the intermediate value theorem

limits at infinity & horizontal asymptotes: part two

limits at infinity & horizontal asymptotes: part one

factoring by grouping and sum/difference of cubes

binomial expansion

multiplying polynomials

adding and subtracting polynomials

graphs of cubic functions