An Integral Part of Memory
Derive This
Partially Implicit
Sketchy Business
Bits & Pieces
100
The rule of for integrating: ∫xndx
xn+1/(n+1) +c
100
d⁄dx ex
ex
100
zx if z=4xy+2x+y2
zx=4y+2
100
Given the sign graph of f'(x), describe what happening at each critical value:
HPI at x=-3
Max at x=0
Min at x=2
100
Evaluate ∫x dx on [1,3]
4
200
The rule of for integrating: ∫ 1/x dx
ln|x|+c
200
The Product Rule
d⁄dxu*v = u*v'+v*u'
200
zxx if z=x3-5y2+4y+1
zxx=6x
200
If f(x)=x4(x-5) and f'(x)=5x3(x-4), what are the critical points?
(0,0) and (4, -256)
200
limx to inf. 1-x/x2+3
0
300
The formula for integration by parts
∫u dv = uv-∫v du
300
How to find average cost, given C(x)
Average cost = C(x)⁄x
300
Differentiate implicitly to find dy⁄dx
2y2=x2-5
dy⁄dx=x⁄2y
300
The critical values of f(x)=x3-3x2+3x+1
x=1
300
Set up u, dv, du, v for Integration by parts for ∫xlnx dx
u= lnx du=1/x dx
dv=x v=x2/2
400
The formula for Producer's surplus
xepe -∫s(x)dx (from 0 to xe
400
The Quotient Rule.
d⁄dx u⁄v= (v*u'-u*v')/v2
400
zxy if z= x2y - 4xy
2x-4
400
the Horizontal and Vertical asymptotes of
y=x2+4/x2
HA: y=1
VA: x=0
400
If C(x)=x2-x, and R(x)=50x, then the Marginal Profit is ________
MP=51-2x
500
Simpson's rule for 6 subintervals
(h/3)[f(x0)+4f(x1)+2f(x2)+4f(x3)+2f(x4)+4f(x5)+f(x6)]
500
The Definition of a Derivative
lim h to 0. (f(x+h)-f(x)) / h
500
Differentiate Implicitly to find dy/dx if
xy2=8
-y/2x
500
If f(x)=x3-x2 and f'(x)=3x2-x, where are the points of inflection?
X=1/6
500
The Equation of the Tangent Line at (1,2) of y=x3+5x2-4
y=13x-9