Limits and Continuity
Differentiation 1
Integration
Parametric Equations, Polar Coordinates, and Vectors
RANDOM!!!!
100
What is the derivative of any constant function?
0
100
If f(x) = c then f'(x) = __
f'(x) = 0
100
What is ∫ ab f(x)dx=F(b)-F(a)
Fundamental Theorem of Calculus
100
What is the position vector?
r(t)= < x(t), y(t)>
100
Who is the first principal of Bronx Science?
Morris Meister
200
What is the name of this theorem?
If ƒ is continuous on a closed interval, then ƒ has both a minimum and maximum on the interval.
Extreme Value Theorem or EVT
200
If f(x) = cot x then f'(x) = __
f'(x) = -csc² x
200
∫ 1/1-x2dx=?
arctan(x)
200
find dy/dx for the curve x=sin t, y=cos t
dy/dx= dy/dt / dx/dt
-sin t/cos t
=- tan t
200
What is the inflection point when dy/dt=ky(1-y/L)?
L/2
300
If f(x)≤g(x)≤h(x) and lim(x→c) f(x)=lim(x→c) h(x)=L, then lim(x→c) g(x) exists and lim(x→c) g(x)=L
What is the Squeeze theorem?
300
If f(x) = arccsc x then f'(x) = __
f'(x) = -1 / (x√(x²-1))
300
What is integration by parts ?
∫ uv'=uv-∫ u'v
300
What is the acceleration vector?
<(d2x/dt2),(d2y/dt2)>
300
Who wrote to Fermat about The Problem of the Points?
Blaise Pascal
400
What are the three reasons why limits don't exist?
1. Infinite Osculation
2. Increases/Decreases without bound
3. The limit from the right does not equal the limit from the left
400
Solve
d/dx f(x)=6x3−9x+4
f′(x)=18x2−9
400
Solve.
∫4xcos(2−3x)dx
−4/3 xsin(2−3x)+4/3∫sin(2−3x)dx
400
What is the arc length in parametric form?
∫ba√ [(dx/dt)2+(dy/dt)2 ]dt
400
What is our current numerical system based on?
Hindu Arabic
500
Lim x→0 √ (x2 + 49 − 7 )/x2 =
1/14
500
Find the derivative of f(y)=(y5−5y3+2y)/y3
f′(y)=2y−4y−3
500
Solve.
∫(4x3−9x2+7x+3)e-xdx
−e-x(4x3+3x2+13x+16)+c
500
What is the formula we use to calculate the area in polar coordinates?
A=1/2∫αβ(r2)dθ
500
Who attended the famous London "coffee house meeting", regarding force at a distance, which went against Aristotle?
Edmond Halley, Hooke, and Wren