Calculus Answers

differentiate implicity the following equations. show complete solutions

1. e^(2x+3y) =x^2 - In(xy^3)

2. x^2 y^3 = xy+x^3 + y^2 + 5

determine the critical points of f(x)=8x³+81x²-42x-8

1.     Determine the critical points of each of 

Find the area bounded by the ff. curves and lines:

1. the loop of y2 = x 4 (3 - x)

2. 4y = x 2 – 2lnx, y = 0, x = 1, x = 4.

3. y 2 + 4x – 8 = 0, Y = 2x

4. an arch of y =1/3sin(x/3)

Find the volume generated by revolving the area bounded by the lines x + y = 5, x = 0

and y = 0, about x-axis.

Find the volume generated by revolving the area enclosed by the curve x2 + y2 = 9 about

the x-axis.

Find the area bounded by the curves y = x3, y = 1, and x = 0 using double integration.

A kite , at a height of 60 ft. is moving

horizontally at a rate of 5ft/sec. away from

the boy who flies it. How fast is the string

being released when 100 ft. are out.

Ship A is travelling south at the rate of 2 km/hr, at the instant that ship B, which is 32 miles south of ship A, is travelling east at rate of 4 km/hr.

a) Are they separating or approaching at the end of 2 hrs, and at what rate? b) At what time are they nearest together?

c) What is their minimum distance apart?

The sides of an equilateral triangle are increasing at the rate of 3 cm/min. Find: a) the rate of change of the perimeter.

b) the rate of change of the area when the side is 3 cm. long.