A/ Find y'. Do not simplify beyond basic algebra.

1) x 2 y 3 - x 5 sin 2y + x y 2 - 5 = 0

2) y = 2 tan x - 4 cos 3y

3) x 2 sin y = y 3 cos 2 x

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B/ 1) Write the equation of the tangent to the curve x ³ y + 7 y ⁴ + x = 4 at P(4, 0).

2) Find c such that c ` (-1, 2) and c satisfies the hypothesis of the
Mean Value Theorem for f (x) = x³ + x - 4.

3) Using differentials approximate the change in the Volume of a sphere
if the radius increases from 2 inches to 2.23 inches. (V= 4/3o r³).

4) One leg of a right triangle increases at 4 cm/sec while the other
decreases at 2 cm/sec. Find the rate at which the hypotenuse is changing
when the first leg measures 5 cm. and the second leg measures 3 cm. (draw a diagram!)

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C/

1) Draw the graph of and list the M₂I₂ACIDS & any other important features for

** Clearly indicate f '(x), f ''(x) and how you found the asymptotes.

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2) Find the vertical, horizontal and oblique asymptotes (if any) for:

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