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36 Cards in this Set

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  • Back
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)