Tangent Lines The Derivative of Parametric Equations
Solution:
The Second Derivative of Parametric Equations Hence to find the second derivative, we find the derivative with respect to t of the first derivative and then divide by the derivative of x with respect to t.
Example Arc Length We can find the arc length of a curve by cutting it up into tiny pieces and adding up the length of each of the pieces. If the pieces are small and the curve is differentiable then each piece will be approximately linear. We can use the distance formula to find the length of each
piece
Example
Solution
Is quite difficult (but not impossible) to do by hand. Either by hand or by computer we get
12.74 Surface Area of Revolution If we revolve a curve around the xaxis what is surface area of the
region that is formed? If we cut the curve into tiny pieces, then each
piece is approximately a line segment, which when revolved around the xaxis
will have area
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