Polar Coordinates
The variables used in polar coordinates.
What are r and theta?
Slope, for a parametric equation.
What is (dy/dt)/(dx/dt)?
The formula for integrating parametric equations.
What is integral(y*dx)?
Fun little note: dx=x'(t)dt or speed*time
The only even prime number.
What is 2?
The polar equivalent of x^2+y^2
What is r^2?
Equation to convert x to polar coordinates.
What is x=rcos(theta)?
How to find a horizontal tangent
What is setting the slope equal to zero?
The parametric formula for arc length.
What is the integral of sqrt((dx/dt)^2 + (dy/dt)^2)dt?
Place of origin of Arabic numerals
Where is India?
The date of Calc 3 midterm 2.
What is February 25, 2022?
Polar equation of a circle with radius 3.
What is r=3?
You find a horizontal tangent at t=a. However, when t=a, the slope = 0/0. This is what you should do next.
What is take the limit of the slope as t approaches a?
The expression of parametric concavity.
What is (dm/dt)/(dx/dt)?
Note: m=slope
The two people who discovered calculus.
Who are Isaac Newton and Gottfried Leibniz?
At what point does
x=2t^2+3
y=t^4
have a horizontal tangent line?
Write the equation 4y^2=x in polar coordinates.
What is r=cos(theta)/(4(sintheta)^2)
also: 4r^2(sin(theta))^2=rcos(theta)
also: r=1/4*cot(theta)*csc(theta)
Find the slope of x=-sqrt(t+1) and y=sqrt(3t)
The concavity of
x=2t^2+3
y=t^4
at t=1.
What is 1/4?
Today's date in Roman numerals.
(mm/dd/yyyy)
What is II/VIII/MMXXII?
Plot (-5, -pi/2) in polar coordinates.
What is (0, 5) in Cartesian coordinates?
Find the Cartesian equation of the curve theta=2pi/3
What is y=-(sqrt3)*x
At what point does
x=t-t^2
y=1+e^-t
have a vertical tangent line?
What is (0.5-0.5^2, 1+e^-0.5)?
Find the length of the arc defined by x=t^3 and y=(3t^2)/2 from 0 to root 3
What is 7?
Euler's first name.
What is Leonhard?
Find the area enclosed by the upper half of the ellipse x=3cost y=2sint
Hints: t is between 0 and pi
1-2(sinx)^2=cos(2x)
What is 3pi?