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40 Cards in this Set

  • Front
  • Back
change in y/change in x
y2 - y1/ x2 -x1
linear function
m is the slope
b is the vertical intercept
exponential function
Po = initial quantity
a = the factor by which P changes when t increases by 1
continuous exponential function
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
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
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)
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
second derivative
f">0, f' increasing, f concave up
f"<0, f' decreasing, f concave down
(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)
(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