Study your flashcards anywhere!
Download the official Cram app for free >
 Shuffle
Toggle OnToggle Off
 Alphabetize
Toggle OnToggle Off
 Front First
Toggle OnToggle Off
 Both Sides
Toggle OnToggle Off
 Read
Toggle OnToggle Off
How to study your flashcards.
Right/Left arrow keys: Navigate between flashcards.right arrow keyleft arrow key
Up/Down arrow keys: Flip the card between the front and back.down keyup key
H key: Show hint (3rd side).h key
A key: Read text to speech.a key
36 Cards in this Set
 Front
 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^n1


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)(xa)
