Calculus Answers

Evaluate I = Z C x^ 2 ydx + (x-2y)dy over the part of parabola y=x^2 from (0,0) to (1,1) 

[DE] Find the Wronskian of the following functions and determine whether it is linearly dependent or linearly independent on (-∞,∞).

1. {x², x+1, x-3}               ans, W=8, linearly independent
2. {3e^2x, e^2x}                     ans, W=0, linearly dependent
3. {x², x³, x⁴}                    ans, W=2x^6, linearly independent

Find the volume in the first octant bounded by x+y+z=9, and the inside cylinder 3y=27-x^3

29. Let f be the function given by ( ) 2 x f x xe− = . From the values of x given below, find a value of x so that the slope of the line tangent to the graph of f at ( xfx , ( )) is equal to 0.2?

The graph of(x²+y²)²=4(x²-y²) shown in the figure is called lemnicate find the points on the graph that correspond to x=1 find the equation of the tangent line to the graph at each point found in point a find the points on the graph at which the tangent is horizontal

Let it be f (x) = 2x³ - 9x² - 10.

a) specify the zeros of the f derivate of the function.

b) with what variable x values does f on grow?

c) determine between the maximum and the minimum value of the function f and [-4, 4].

6. 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?

5. A spherical snowball with an outer layer of ice melts, so that the radius of the snowball

decreases at the rate of 1/5 cm/sec. Find the rate at which the volume decreases when the

diameter is 50 cm.

3. An open rectangular box w/ square ends to hold 6400 cu ft, is to be built at a cost of

Php 75.00 per sq ft. for the base and

Php 25.00 /sq ft for the sides. Find the most economical dimensions.

2. A boy is flying a kite at a height of 150 ft. If the kite moves horizontally away from the

boy at the rate of 20 ft/sec, how fast is the string being paid out when the kite is 250 ft from him?