CALCULUS I ASSIGNMENT #3 |

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

1) xsin^{ 2 }y^{ 3} - x^{ 5} 2y + x y^{ 2} - 5 = 0 |
2) y = 2 tan x - 4 cos 3y |
3) xsin^{ 2} y = ycos^{ 3} ^{ 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

2) Find *c* such that *c* ` (-1, 2) and *c* satisfies the hypothesis of the

Mean Value Theorem for *f (x) = x ^{3} + 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 r^{3}).

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 **M _{2}I_{2}ACIDS** & 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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