Presentation: Uma Quizizz: Anna 5n1: Emma

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Presentation transcript:

Presentation: Uma Quizizz: Anna 5n1: Emma P a r a m e t r i c s & V E C T O R S Presentation: Uma Quizizz: Anna 5n1: Emma

What will be Covered Parametrics Vectors Graphing Eliminating the Parameter Finding the derivative Finding the second derivative Arc length in parametric Vectors PVA Speed of a particle Total distance traveled

P A R A M E T R I C S

Graphing Parametric Equations Create a table of values for x, y, and t and insert selected values of t Plug t values into given x and y equations and put solved x and y values into table Use x and y values to graph the parametric

In the Calculator Mode → Parametric Y= Type in x and y equations

Eliminating the Parameter Use the x equation to solve for t Plug the expression equal to t in for t in y equation

Finding Divide the derivative of y by the derivative of x Find the line tangent to the graph at

Finding 12 Determine concavity at ( 2 , 3 ) The second derivative of y over the first derivative of x 12

Arc Length Find the length of the curve from ~1.317

V E C T O R S

Position < x(t) , y(t) > Usually the first equations given in a question which can be derived to find velocity

Velocity < x’(t) , y’(t) > The derivative of position, used to find: Total distance traveled Speed of the particle (magnitude of velocity vector) Acceleration (derivative)

Acceleration < x”(t) , y”(t) > The derivative of velocity Most commonly used to determine if the particle is speeding up or slowing down at a given point (whether velocity and acceleration have the same sign or not)

PVA Practice The position of a particle at any time Is given by Find the magnitude of the velocity vector at time t = 5 Find the total distance traveled by the particle from t = 0 to t = 5 Find dy/dx as a function of x

Resources apcentral.collegeboard.org Barron’s Panther Creek AP Calculus website Past tests