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Implicit curve

bccalcclassact5bparametric

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Name:________________________ Date:________________________ AP Calculus BC Class Activity 5b: Parametric Equations and Calculus Find the derivative for the following parametric equations: x = t2 + 1 and y = 2t3 ? t2 x = 3 sin t and y = 4cos t ? 1 Find the second derivative for the following parametric equations: x = t2and y = t2 + 6t + 5 x = ln t and y = t2 + t A curve C is defined by the parametric equations x = t2 + t ? 1 and y = . Find in terms of t. Find an equation of the tangent line to C through the point where t = 2. A curve C is defined by parametric equations x = t2 ? t + 1 and y = t3 ? 3t. Find all points where the tangent line is horizontal. Find all points of vertical tangency.

bccalcclassact5aparametric

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Name:________________________ Date:________________________ AP Calculus BC Class Activity 5a: Parametric Equations Complete the value of table below and graph the curve for and y = t x y -2 -1 0 1 2 3 Complete the table below and graph the curve for and . t x y 0 ? 2? For the following problems eliminate the parameter and find y as a function of x. and and Given the function below and an equation for x, find one parametric curve that could represent it: and and Use
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