10.2 Tangents and AreasIfwehaveparametricequationsx=f(t), y=g(t)and we substitute y=F(x),then we have g(t)=F(f(t)).Now, if g,F, and fare differentiable functions, the Chain Rule can be used to find g’(t). '( )'(( ))))Slope of the tangent to () at ( ,()) is )0gtgtFftfxft FxftyFxxFxFxdydydxdtdxdxdtdt=⋅=⋅⇒===≠Example: Find an equation of the tangent line at t=1 for the curve . 321,3xtytt=−= − +1tExample: Find an equation of the tangent to the curve at (3,4) (a) without eliminating the parameter and (b)
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This note was uploaded on 01/20/2012 for the course MATH 2057 taught by Professor Estrada during the Fall '08 term at LSU.