c10s2 - 10.2 Tangents and Areas If we have parametric...

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10.2 Tangents and Areas If we have parametr ic equat ions 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 gt g tF f tf x f t F x ft yF x x F x Fx dy dy dx dt dx dx dt dt =⋅ = = = =≠ Example: Find an equation of the tangent line at t=1 for the curve . 32 1, 3 xt y t t =− = − + 1 t Example: Find an equation of the tangent to the curve at (3,4) (a) without eliminating the parameter and (b)
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