Calculus

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.

Name: ____________________ Date: ____________________ AP Calculus BC Class Activity 4c: Differentials Given , use a tangent line through to approximate g (1.1) to three decimal places. Use calculus to approximate . The measurement of an edge of a cubic box is found to be 12 inches with a possible error of inch. Use differentials to find the greatest possible error in calculating the volume of the box. The radius of a spherical balloon is measured to be 6 inches. . The possible error in calculating the radius is 0.2 inches. Use differentials to find the greatest possible error in calculating the volume of the sphere. Find the largest possible value for the actual volume of the spherical balloon.

Name:________________________ Date:________________________ AP Calculus BC Class Activity 4a: Concavity For the function , find and show where it is concave up on [0, 2?]. Find and show the points of inflection for the function . Find and show the points of inflection for the function . Given the function : Find the critical points for p (x), i.e. the candidates for local maximums and minimums. Use the second derivative test to show which points are maximums and which are minimums. Given the following graph for : Notate the intervals where f (x) is concave up. Notate the intervals where f (x) is concave down. Notate the points of inflection. Given the following graph for : Notate theintervals where g (x) is concave up.

Name:________________________ Date:________________________ AP Calculus BC Class Activity 3a: Extrema Find the critical points for the following functions: 4. Given , find the absolute maximum and absolute minimum on the interval . 5. Given , find the absolute maximum and absolute minimum on the interval . 6. Find and show the local maximums and local minimums for the function 7. Find the interval(s) for which the following function is increasing: 8. Find and show the local minimums and local maximums for given
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Name:________________________ Date:________________________ AP Calculus BC Class Activity 1b: L?Hopital?s Rule Use L'Hopital's Rule to evaluate the following:
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