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### 36 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)