What is the first derivative of a parametric function?
100
The area of a loop r= 2+4cosθ on the interval [2π/3, 4π/3]
What is 2.174?
100
The derivative of y= 3t^2 and x= 5cosθ
What is 6t/-5sinθ?
100
The arc length given y= ln(secx) on the interval [0, pi/4]
What is ln(√2+1)
100
1/2 ∫ f(x) dx
on the interval from [α,β]
What is the formula area of a polar curve?
200
Y= rsinθ
X= rcosθ
What is the formula for the conversion from parametric to polar form?
200
The values of x for which of the graphs r= 1+ cosθ and r= 1- sinθ intersect
What is 3π/4, 7π/4, 0?
200
The acceleration vector for when the position of a particle is given by y= ln(4x^3- 2) and x= 6x
What is (-4x-48x^4)/(4x^3-2)^2?
200
The acceleration of a particle moving in the xy-plane so that the position of the particle at any time t is
given by
x(t) = 2e^3t + e^-7t and y(t) = 3e^3t - e^-2t
What is <6e^(3t) - 7e^(-7t), 9e^(3t) + 2 e^(-2t)>?
200
The acceleration of a particle moving in the xy-plane so that the position of the particle at any time t is
given by
x(t) = 2e^3t + e^-7t and y(t) = 3e^3t - e^-2t
What is <6e^(3t) - 7e^(-7t), 9e^(3t) + 2 e^(-2t)>?
300
√[(dy/dt)^2+(dx/dt)^2 )]
What the speed of a parametric function at a given value t?
300
The area of a polar curve r= 1 + cos 4θ on the interval [π/4, -π/4]
What is π/8?
300
The second derivative if
x = t - t^2
y = t – t^3
What is (1 - 3t^2)/(1-2t)?
300
(d^2y)/(dx^2) when x(t)=t^3+t and y(t)=t^5+1
What is (30t^5+20t^3))/(3t^2+1)^3
300
The equation of the tangent line to the curve r =2+2 sin θ when θ = pi/4
What is y-(√2+1)= (-1-√2)(x-(√2+1))?
400
1/2 ∫ f(x) dx
on the interval from [α,β]
What is the formula area of a polar curve?
400
The area inside r = 3 + 2 sinθ and outside r= 2
What is 24.187?
400
the equation of the tangent line to the curve r =2+2 sin θ when θ = pi/4
What is y-(√2+1)= (-1-√2)(x-(√2+1))?
400
The length of a curve when y(t)=(1/3)(t^2+2)^(3/2)
What is 12?
400
The second derivative if
x = t - t^2
y = t – t^3
What is (1 - 3t^2)/(1-2t)?
500
[(d/dt)(dy/dx)]/ (dx/dt)
What is the second derivative of a parametrc function?
500
The area of the region outside r = 3 + 2 sinθ and inside r = 2
What is 2.196?
500
dr/dθ (3+8cosθ )
What is (16cosθsinθ+3cosθ)/(8cos^2θ-3sinθ-8sin^2θ)
500
Position of a car after one second when velocity is given by and position at t=1 is 3