c10s2

# c10s2 - the parameter first for 5cos 5sin x t y t = = The...

This preview shows page 1. Sign up to view the full content.

10.2 Tangents and Areas If we have parametric equations  x=f(t) , y=g(t) and we substitute y=F( x ), then we have g(t)=F( f(t)) . Now, if g,F, and f are  differentiable functions, the Chain Rule can be used to find g’(t). '( ) '( ) '( ( )) '( ) '( ) '( ) '( ) '( ) Slope of the tangent to ( ) at ( , ( )) is '( ) 0 g t g t F f t f t F x f t F x f t y F x x F x F x dy dy dx dt dx dx dt dt = = = = = Example: Find an equation of the tangent line at t=1 for the curve   3 2 1 , 3 1 x t y t t = - = - + . Example: Find an equation of the tangent to the curve at (3,4)  (a)  without eliminating the parameter and (b)  by eliminating
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: the parameter first for 5cos , 5sin x t y t = = . The second derivative can be used to find concavity. 2 2 d dy d y d dy dt dx dx dx dx dx dt = = Example: Find the second derivative for 2cos , sin 2 x t t y t = + = . Example: Find the points on the curve where the tangent is horizontal or vertical for 3 2 3 3 , 3 x t t y t t =-=-....
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online