Calculus Answers

If
f(x,y)=tan−1yx
f(x,y)=tan−1⁡yx
, find
fx

Suppose that water is pouring into a swimming pool in the shape of a right circular cylinder at a constant rate of 44 cubic feet per minute. If the pool has radius 44 feet and height 99 feet, what is the rate of change of the height of the water in the pool when the depth of the water in the pool is 55 feet?

The original function used to model the cost of producing x PortaBoys Game Systems was
C(x) = 80x + 150.
While developing their newest game, Sasquatch Attack!, the makers of the PortaBoy revised their cost function using a cubic polynomial. The new cost of producing x PortaBoys is given by
C(x) = .03x3 − 4.5x2 + 227x + 250.
Market research indicates that the demand function
p(x) = −1.5x + 250
remains unchanged. Find the production level x that maximizes the profit made by producing and selling x PortaBoys. (Round your answer to the nearest whole number.)

Let
y=3x2−2x⋅4x3−4x2⋅73x+4

(a) Given that ln(y) can be written in the form
ln(y)=ln(A)x3+ln(B)x2+ln(C)x+ln(D).

What are the coeffcients A, B, C, and D?
A=

B=

C=

D=

(b)
Using the correct answer to (a), find the value of dy/dx when x=0

If f(x)=(arctan(x))4+3arctan(x)+5,
then f′(x)=

If f(x)=x3+2cos(x)3sin(x), find f′(π2).

Assume f(x)is a function differentiable at the points 0 and 1 with
f(0)=-2, f′(0)=-1, f(1)=1 and f′(1)=0,
and assume F(x)=f(sin(x)).

Compute
f'(0)=
f'(pi/2)=

Let y6+x2y5=e4x
Then dy/dx=

The electric current i flowing in a device varies with time t . The equation linking the two variables is as follows

i=2sin(5t)

The area under the graph represents the charge q that has passed over any given time interval

Calculate the area and hence the charge by intergrating the equation between t=t1 and t=t2
t1=o.4 and t2=0.5

Given the equation of the circle x^2+y^2=225,Find
dy/dx
The equation of the tangent to the circle x^2+y^2=225 at the point (3,4)