Vector Kinematics
They are the unit vectors for the Cartesian x, y, and z, in that order.
What are i-hat, j-hat, and k-hat?
They are the two endpoints of the interval
abs(x+7)=12
What are 19 and -5?
Estimating a rate of change from a data table.
What is Average rate of change used for?
Hamlet: "To be, or not to be. That is the..."
What is "question"?
The status of the green 2022 Prius?
What is it total loss due to a crash?
It's what you have to do to a vector position function in three dimensions to find the velocity vector function.
What is taking all three derivatives and leaving the unit vectors there?
It's the radius of convergence of the series
sum_(n=0)^infty(x-3)^n/5^(n+1)
What is 5?
Estimating the total amount of something from a data table about its rate of change.
What is a Riemann sum used for?
Romeo and Juliet: "A rose by any other name would smell as..."
What is "sweet"?
The status of the 2024 Prius
Natalie is driving it in Washington
It's how you calculate the distance from the origin.
What is using Pythagorean Theorem on the components of the position function?
For the error bound of a Taylor Series, it's what determines where the center of the error-bound interval is.
What is the place where the series was written?
Finding the maximum or minimum value of something on a closed interval.
When do you use the Extreme Value Theorem?
Macbeth "Double, double, toil and..."
What is "trouble"?
The status of the grey 2010 Prius.
What is Mrs. Finander drives it every day?
It's how you find the speed.
What is using Pythagorean Theorem on the velocity vector?
For the error in an alternating series, it's what determines the RADIUS of the interval.
What is the value of the first unused term?
Finding how fast the radius of a sphere is growing when you how how the volume is changing.
What is related rates?
Julius Caesar "Friends, Romans, Countrymen/Lend me your..."
What is "ears"?
The 1969 silver Camaro convertible
Mrs. Finander's former brother-in-law has it.
Everything you need to do to find the magnitude of the acceleration at a certain time starting from the position function.
What is differentiate twice, plug the number in, and use Pythagorean Theorem?
It's what we use in the Lagrange Error Bound instead of the value of the relevant derivative at the center of the interval.
What is the largest that the relevant derivative can be in that neighborhood?
Richard III: "Now is the winter of our..."
What is "discontent"?
The total number of cars that Mrs. Finander has owned or sort-of owned.
What is 9?