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### 40 Cards in this Set

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 slope rise/run change in y/change in x y2 - y1/ x2 -x1 linear function y=mx+b m is the slope b is the vertical intercept exponential function P=Poa^t Po = initial quantity a = the factor by which P changes when t increases by 1 continuous exponential function P=Poe^kt inverse function a function has an inverse if its graph intersects any horizontal line at most once (horizontal line test) graph is a reflection about the y=x line log10x=c 10^c=x ln x = c e^c = x Properties of Natural Logs ln(AB) = lnA + ln B ln(A/B) = ln A - ln B ln(A^p) = p ln A ln e^x = x e^ln x = x ln 1 = o ln e = 1 f(t) = A sin (Bt) abs A = amplitude 2`/ abs B = period (in tangent period = `/abs B) inverse of a trig function arc trig function continuous function no breaks, jumps or zeros (don't pick up pencil) Intermediate Value Theorem f is continous on closed interval A,B. If k is any number between f(a) and f(b), then there is at least one number c in A,B such that f(c)=k average velocity change in position/change in time s(b) - s(a) / b - a instanteous velocity 1) at t=a lim h->0 s(a+h) - s(a)/ h 2)the average velocity over an interval as the inverval shrinks around a 3) slope of the curve at a point(tangent line) Properties of Limits lim k =k lim x->c x = c limits with infinity 1)limit of 3x = infinity when x approaches infinity 2) limit of 1/3x = o when x approaches infinity 3) limit of 3x/4x = 3/4 when x approaches infinity average rate of change of f over the interval from a to a+h f(a+h) - f(a)/h (general formula while equation with s was specifically for height) derivative instanteous rate of change lim h->0 f(a+h) - f(a)/ h slope of the tangent line rules of derivatives f'>0, f increasing f'<0, f decreasing f(x) = k, f'(x) = 0 power rule f(x)=x^n, then f'(x) = nx^n-1 interpretations of the derivative dy/dx second derivative f">0, f' increasing, f concave up f"<0, f' decreasing, f concave down d/dx(e^x) e^x d/dx(a^x) (ln a)a^x Product Rule (fg)' = f'g + fg' Quotient Rule (f/g)' = f'g -fg'/g^2 Chain Rule d/dx(f(g(x)) = f'(g(x))*g'(x) d/dx(sin x) cos x d/dx(cos x) -sin x d/dx(tan x) 1/cos^2 x d/dx(ln x) 1/x d/dx(a^x) (ln a)a^x d/dx(arctan x) 1/1 + x^2 d/dx(arcsin x) 1/sqrt(1- x^2) implicit functions if there is a y use y' tangent line approximation f(x) = f(a) + f'(a)(x-a) Mean Value theorem f'(c) = f(b) - f(a) / b-a sigma notation definite integral number at the top tells the number of intervals number at the bottom tells where to begin global max and min overall maximum and minimum highest and lowest y values substitute the cp into the f(x) set equal to zero to find y location on the graph to see which is the highest definite integral F(b) - F(a) = integral from b to a F'(t) dt