The Catholic University of America Calculus Problems


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(1 point) Write the parametric equations
T = 4t – tủ, g = 4 – 2t
in the given Cartesian form.
L =
(1 point) The following parametric equations trace out
a loop.
x=4 – t?
-243 + 3t+1
Find the t values at which the curve intersects itself.
t +

Find the r and y values of the intersection.
Graph the curve on a calculator. Turn in a sketch of
the curve.
(1 point) If x = 4t4 + 3 and y = 5t – t?, find the
following derivatives as functions of t.
dy/dx =
(1 point) Given the parametric equations
x = 3t + 2,
y = sin?(3t)
Write the derivative dy/dx as a function of t.
(1 point) If 3t + t2 and y = 6 – 5t, find an
equation of the tangent (in terms of r and y) to the
curve at t
Tangent line:

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