Section 1
Preview this deck
Circular Cross-Sections
Front
| 5 | 0 | ||
| 4 | 0 | ||
| 3 | 0 | ||
| 2 | 0 | ||
| 1 | 0 |
Active users
0
All-time users
0
Favorites
0
Last updated
6 years ago
Date created
Mar 14, 2020
Cards (51)
Section 1
(50 cards)
Circular Cross-Sections
V=π/4∫(top function-bottom function)^2 dx
Rectangular Cross-Sections
V=∫(top function-bottom function)(height) dx
Arc Length
Taylor Series
Velocity, Speed, Acceleration
Speed increases when v(t) and a(t) have the same sign, decreases when opposite signs.
Harmonic Series
Trapezoidal Rule
Comparison Test
Isosceles Right Triangle Cross-Sections (hypotenuse in XY plane)
V=1/4∫(top function-bottom function)^2 dx
Power Series
Second Fundamental Theorem of Calculus
Limit Comparison Test
Intermediate Value Theorem
Integration by Parts
∫vdu is easier to solve than original ∫udx = uv − ∫vdu .
Volume of Solids of Revolution
V=π∫(furthest from a.r-a.r)^2-(closest from a.r-a.r)^2dx
lim→∞ln(n)/n =
0
Extreme-Value Theorem
Arc Length in Parametric form
Derivative of an inverse function
1/(g'(g^-1(x))
Distance
Equilateral Cross-Sections
V=√3/4∫(top function-bottom function)^2 dx
lim→∞x^n/n! =
0
Arc Length in Polar Form
tangent line equation (Linear Approximation)
Average Value
Mean Value Theorem
Fundamental Theorem of Calculus
Isosceles Right Triangle Cross-Sections (leg in the XY plane)
V=1/2∫(top function-bottom function)^2 dx
Square Cross-Sections (diagonal in XY plane)
V=1/2∫(top function-bottom function)^2 dx
The n-th Term Test
lim→∞an ≠ 0 then the series diverges, the converse is false
ln(x)<0
when 0<x<1
Geometric Series
Logistics
dY/dT= ky(1-Y/L) L: carrying capacity (maximum); horizontal asymptote. L/2: max rate
P-series
∑1/(n^p) p>1 Converges p≤1 Diverges
Average Rate of Change
Euler's Method
Yn= Yn-1 + hF(Xn-1, Yn-1)
Area in Polar Coordinates
A=1/2∫(f(θ)^2)dθ = 1/2∫(r^2)dθ
Square Cross-Sections
V=∫(top function-bottom function)^2 dx
Semi-Circular Cross-Sections
V=π/8∫(top function-bottom function)^2 dx
Area Between Curves
[top-bottom]dx [right-left]dy
Integral Test
Instantaneous rate of change
L'hopital's Rule
lim→∞ⁿ√n =
1
Definition of Derivative
Speed
magnitude of velocity
lim→∞x^(1/n) =
1
Ratio Test
Cartesian vs. Polar Coordinates
x=rcos(θ) y=rsin(θ) x²+y² tan⁻¹(y/x)
Alternating Series
also test: |a n+1|≤ |a n|
Section 2
(1 card)