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Indeterminate Form
Parametric
Polar
Vector
Infinite Series
100
When you cannot determine the limit by direct substitution
What is indeterminate form
100
Formula of the first derivative of a parametric equation given: x=f(t) y=g(t)
What is (dy/dt)/(dx/dt)
100
The two variables used in a polar equation
What is r and θ
100
The component form of a vector
What is (a,b) where a is the x-component and b is the y-component
100
Formula for the infinite sum of an infinite series when =a[r^(n-1)]
What is a/(1-r)
200
The way in which you find limits that approach infinity when the answer is in indeterminate form
What is L'Hopital's Rule
200
Formula of the second derivative of a parametric equation given: x=f(t) y=g(t)
What is [dy/dx]'/(dx/dt)
200
The equations used to convert from polar form to vector form
What is x=rcos(θ) y=rsin(θ) x^2+y^2=r^2 or r=√[x^2+y^2]
200
Formula for the magnitude of a vector
What is |v|=√[x^2+y^2]
200
The condition where an infinite geometric series diverges
What is |r|>1 or |r|=1
300
Find the limit as x-->0 of (3x-sinx)/x
What is 2
300
The equation for arc length of a parametric equation
What is L=∫√ [(dy/dt)^2+(dx/dt)^2] dt
300
The derivative (dy/dx) using polar equations
What is dy/dx=[f'(θ)sin(θ)+f(θ)cos(θ)]/ [f'(θ)cos(θ)-f(θ)sin(θ)]
300
Dot Product when u=(a,b) and v=(c,d)
What is u⋅v=ac+bd
300
The expanded series for the Maclaurin Series of e^x
What is 1+x+x^2/2!...+x^n/n!
400
lim x-->0 (l-x)^(2/x)
What is e^-2
400
Rewrite the following parametric equations by eliminating the parameter (make it so it is just x and y variables; no t): x=2cost y=2sint
What is x^2 + y^2 = 4
400
Area of region between the origin and the curve r=f(θ)
What is A=∫(1/2)(r^2)dθ
400
Angle between the two vectors u=(a,b) and v=(c,d)
What is θ= cos^(-1) [(u⋅v)/(|u|⋅|v|)]
400
The conditions of divergence when using the nth-term test
What is lim as x-->∞ ≠ 0 (if the limit is finite or ∞, then it is divergent)
500
limit as x-->0 of (sinx)^x
What is 1
500
Surface area formula for a revolution about the x-axis given x=f(t) and y=g(t)
What is ∫2π g(t) √ [(dx/dt)^2+(dy/dt)^2] dt
500
Formula for the length of a polar curve
What is L=∫√[r^2-(dr/dθ)^2]dθ
500
Find the unit vector tangent to the parametrized curve when x=1/t and y=3t at the point where t=2
What is <1/√[145],-12/√[145] >
500
The conditions for which an alternating series is convergent
What is lim as x-->∞ of a=0 when 0 < a(n+1) and a(n+1) < or = a(n) *a sub (n+1) and *a sub n