Find The solution of the Differential Equation of (y+4x+2)dx - dy = 0, y(0) = 3 ( Please With Steps)

Make an investigate about others method may be used for linearization. Apply and explain in shorts words.

Analyze the function f and sketch the curve of f by hand. Identify the domain, x-intercepts, y-intercepts, asymptotes, intervals of increasing, intervals of decreasing, local maximums, local minimums, concavity, and inflection points. f(x) = ((x−1)^3)/(x^2)

Find

(f ⁻¹)'(a).

f(x) = 6 + x² + tan(πx/2),    −1 < x < 1,    a = 6

1. Average Cost for Producing Microwaves

Let the total cost function C(x) be defined as follows.

C(x) = 0.0003x³ − 0.02x² + 103x + 3,600

Find the average cost function C.

C(x) =

Find the marginal average cost function C '.

C '(x) =

2. Marginal Revenue for Producing Loudspeakers

The management of Acrosonic plans to market the ElectroStat, an electrostatic speaker system. The marketing department has determined that the demand for these speakers is represented by the following function, where p denotes the speaker's unit price (in dollars) and x denotes the quantity demanded. Find the following functions (in dollars), find the value (in dollars) and interpret your results.

p = −0.02x + 890      (0 ≤ x ≤ 20,000)

(a)

Find the revenue function R.

R(x) =

(b)

Find the marginal revenue function R'(x).

R'(x) =

(c)

Compute the following value.

R'(8,200) =

Interpret your results.

When the level of production is  units, the production of the next speaker system will bring an additional revenue of  dollars.

3.Marginal Cost, Revenus, and Profit for Producing LCD TVs

A company manufactures a series of 20-in. flat-tube LCD televisions. The quantity x of these sets demanded each week is related to the wholesale unit price p by the following equation.

p = −0.007x + 190

The weekly total cost (in dollars) incurred by Pulsar for producing x sets is represented by the following equation. Find the following functions (in dollars) and compute the following values.

C(x) = 0.000001x³ − 0.02x² + 140x + 75,000

(a)

Find the revenue function R.

R(x) =

Find the profit function P.

P(x) =

(b)

Find the marginal cost function C'.

C'(x) =

Find the marginal revenue function R'.

R'(x) =

Find the marginal profit function P'.

P'(x) =

(c)

Compute the following values. (Round your answers to two decimal places.)

C'(1,500)=R'(1,500)=P'(1,500)=

20) For the given cost function C(x)=22500+800x+x2,

First, find the average cost function. Use it to find:

a) The production level that will minimize the average cost?

21) Given the function f(t)=(t−3)(t+7)(t−6).

its f-intercept is  

its t-intercepts are

b) The minimal average cost?

1. The position of a particle moving in a straight line during a 5–second trip is s(t) = 2t² − 2t + 2 cm. Find a time t at which the instantaneous velocity is equal to the average velocity for the entire trip beginning at t = 0.

2. a) A particle moving along a line has position s(t) = t⁴ − 34t² m at time t seconds. At which non negative times does the particle pass through the origin? (Enter your answers as a comma-separated list. Round your answers to two decimal places.)

b) At which nonnegative times is the particle instantaneously motionless (that is, it has zero velocity)? (Enter your answers as a comma-separated list. Round your answers to two decimal places.)

3. The tangent lines to the graph of f(x) = 7x² grow steeper as x increases. At what rate do the slopes of the tangent lines increase?

Find the directional derivative of a funtion f(x,y,z)=x^2+e^xyz at point P(1,0,2) in the direction from P to Q (1,1,1). is this max rate of change ?

a- Give an example equation of each of the common surfaces in this course (plane, sphere, cylinder, cone, paraboloid) and describe feature(s) that distinguish its graph from the others.

b- If you want to determine an equation of a line that passes through the point (0,0,1) and that is parallel to the xy-plane, how many such lines are possible and what do they all have in common? Give equations of at least two DIFFERENT such lines are part of your response.

1. For the function f(x)=x2−36 evaluate f(x+h).

f(x+h)=

2. Let f(x)=3x+4,g(x)=9x+12, and h(x)= 9x^2+ 24x+16. evaluate the following:

a. (fg)(3)=

b. (f/g) (2)=

c. (f/g) (0)=

d.(fh)(-1)=

3. Let f(x)=2x-1, g(x)=x-3, and h(x) =2x^2-7x+3. write a formula for each of the following functions and then simplify

a. (fh) (x)=

b. (h/f) (x)=

c. (h/g) (x)=

4.Let f(x)=5−x and g(x)=x^3+3 find:

a. (f∘g)(0)=

b.(g∘f)(0)=

c. (f∘g)(x)=

d. (g∘f)(x)=

5. Let f(x)=x^2+5x and g(x)=4x+5 find:

a. (f∘g)(x)=

b. (g∘f)(x)=

c. (f∘g)(0)=

d. (g∘f)(0)=

6. Let f(x)=x^2 and g(x)=x−5 find:

a. (f∘g)(x)=

b. (g∘f)(x)=

c. (f∘g)(5)=

d. (g∘f)(5)=

Determine the centroid C(x,y,z) of the solid formed in the first octant bounded by z=16-y and x^2=z.

Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

f(x, y) = x^3 + y^3 − 3x^2 − 9y^2 − 9x

local maximum value(s):

local minimum value(s):

saddle point(s) (x, y, f) =

1. Find all the values of x such that the given series would converge.
∞∑n=1 (3x)^n/n^11
The series is convergent
from x =     , left end included (enter Y or N):
to x =     , right end included (enter Y or N):

2. Find all the values of x such that the given series would converge.
∞∑n=1 5^n(x^n)(n+1) /(n+7)
The series is convergent
from x= , left end included (enter Y or N):
to x= , right end included (enter Y or N):