Calculus Answers

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. (2 points)

3, -13, and 5 + 4i

differentiate following functions:
1. y= 2x^2e^2x
2.y= (x^2 -2) / (x^2 +2)
3.y= 2sin(3x^2 + 2x)

Evaluate each of the following function at given values of the independent variables.
1. f(t)=t/f^2-1
Find:
a. f(-x)
b. f(t-2)
c. -f(2/x)
2. R(y)=(n^2y-sin^2y)
Find:
a. R(0)
b. R(pi)
c. R(-pi)
d. R(pi/2)
e. R(pi/3)
f. R(pi/4)
g. R(pi/6)
h. R(pi-x)
i. R(pi/2 +x)
j. R(pi+x)
3. g(x)=2^y-2^-y
Find:
a. g(2)
b. g(-1)
4. f(x)=3^x-1
Find:
f(1)+f(2)
5. if f(x)=1/square root of x-1
Find:
f(x)-f(2)/x-2

#51. Revenue: Assume that a demand equation is given by q=5000-100p. Find the marginal revenue for the following production levels (values of q). (Hint: Solve the demand equation for p and use R(q) =qp.)
a.1000 units
b.2500 units
c. 3000 units

#52. Profit: Suppose that for the situation in excercise 51 the cost of producing q units is given by C(q)=3000-20q+0.03q^2. Find the marginal profit for the following production levels.
a. 500 units
b.815 units
c.1000 units

my problem is i need to find the dy/dx for the problem. Xcubed+2Ycubed-3XsquaredYsquared
+6Xsquared-3XYsquared+5=0 please help me with this problem.

Give an example of a situation in which composite differentiation might be used. Give examples of functions that might be applicable in your situation, and show how the relevant rates of change might be calculated.

Given that
A=sinti+costj+tk
A=sin⁡ti+cos⁡tj+tk
, evaluate
∣∣∣d2Adt2∣∣∣
A particle moves along a curve whose parameter equations are
x=e−t
x=e−t
,
y=2cos3t
y=2cos⁡3t
,
z=2sin3t
z=2sin⁡3t
. Find the magnitude of the acceleration at t=0
A particle moves along the curve
x=2t2
x=2t2
,
y=t2−4t
y=t2−4t
and
z=3t−5
z=3t−5
,where t is the time. Find the components of the velocity at t=1 in the direction
i−3j+2k

Continuous Money Flow. Find the total income in 8 years by a continuous money flow with a rate of f(t) = e0.06t and the present value in 8 years with r = 10%.

Plutonium-240 decays according to the function


where Q represents the quantity remaining after t years and k is the decay constant, 0.00011... How long will it take 36 grams of plutonium-240 to decay to 12 grams?

If
ϕ=2xz4−x2y
ϕ=2xz4−x2y
, find
|▽ϕ|