Formulas
(dy/dt)/(dx/dt)
What is the first derivative of a parametric function?
"(derivative of y) / (derivative of x)"
NO L'HOPITAL!
The area of a loop r= 2+4cosθ on the interval [2π/3, 4π/3]
What is 2.174?
The derivative of y=t3 and x=t2-3t
What is 3t2/(2t-3)
The quadrant containing the point (-3, -pi/3)
What is quadrant 2
1/2 ∫ f(x) dx on the interval from [α,β]
What is the formula area of a polar curve?
the distance traveled by a particle, also arc length, parametrically speaking
What is the integral, from a to b, of (√[(dy/dt)^2+(dx/dt)^2 )])
The second derivative of x=1/t and y=-2+ln(t)
What is t3
The cartesian equivalent of theta = 5pi/6
What is y = [-sqrt(3)/3] x
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)>?
The speed of a parametric function, also the magnitude of the velocity vector
What is √[(dy/dt)^2+(dx/dt)^2 )]
The cartesian equivalent for r = 12/(-4cos(theta)+6sin(theta))
What is y=(2/3)x + 2
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))?
the four conversion equations between polar and cartesian
What is x=r*cos(theta), y=r*sin(theta), r2=x2+y2, tan(theta)=y/x
The area inside r = 3 + 2 sinθ and outside r= 2
The area of the region outside r = 3 + 2 sinθ and inside r = 2
What is 24.187?
What is 2.196?
The value of dy/dx for r = 2+3sin(theta) when theta = 3pi/2
What is 0
The coordinates for the center of the circle r = 2cos(theta)
(1, 0)
the second derivative of a parametric function
[(d/dt)(dy/dx)]/ (dx/dt)
What is [(d/dt)(dy/dx)]/ (dx/dt)
"(the second derivative) / (the first derivative of x)"
NO L'HOPITAL!
The point of horizontal AND vertical tangency for r=1+sin(theta)
What is no point exists
The derivative of r=3+8cosθ
What is [-16sin(theta)cos(theta)-3sin(theta)]/[-16sin(theta)cos(theta)-3sin(theta)]
Nine standard graph shapes found in polar functions
What are lines, circles, ellipses, cardiods, limacons, limacons with an inner loop, rose, archimedian spiral, lemniscate, conic section