Cale3 Final Take Home (18F) NAME Due Tuesday (Dec 18) (Show exact value and Show all your work) 1 . Find the volume of the solid E between z 3 x2 + уг) (a cone) and z-f ID x2-y2 (a semi-sphere) by (by any coordinates) evaluating the triple integral Vlldv

Q: How do I solve this Bernoulli equation using P(x), Q(x) and n as well as u(y)?

A: First, we write it in form of Bernoulli Differential equation. 

Q: I don’t understand what I am doing wrong. Please help me find the tangent line equation!

A: To calculate the slope and equation of the tangent line from the provided value of parameter which i...

Q: Do the domain of the following function:

A: Consider the provided function.

Q: Logarithmic Differentiation - See attachment

A: Find the derivative of the given function.

Q: find the volume aquired by taking by region bound by  y=x^2 and  y=x^4 and rotating it around x=-1

A: To calculate the volume bounded by the curve y=x2 and y=x4 which is rotating about the line x=-1. No...

Q: 3x4 y‴+9x4 =5xy′+5x5 y″+9lnx   Determine the order of the differential equation shown above.

A: The given differential equation is,

Q: 15. A dinghy is pulled toward a dock by a rope from the bow through a ring on the dock 6 feet above ...

A: I have made use of the diagram in the question and added additional labels. Please see the white boa...

Q: Suppose that a particle has been shot into the air in such a way that the rate at which its height i...

A: v = 320 - 32tIf h represents the height of the particle at any time t, then:v = dh / dt = 320 - 2t

Q: How can I get the result? Which is the result?

A: (a)we are given a function 

Q: I need help with this please. How do I find the volume generated by revolving the region bounded by ...

A: Given information:The region bounded by y = -sinx and y=0, from x= -2pi to x=0, about the x-axis

Q: Hello,  I need help explaining how pi(k)/2 came about, I know where pi/4 came from. Thank you for th...

A: Consider the provided trigonometry equation.

Q: Hello,  How do I know when the limit is since it is not going by pi/6, pi/4, pi/3, pi/2, pi, and 2pi...

A: As a first step I will respond to your specific question "What is the limit? Or how do i know when t...

Q: How do I solve this differential equation using P(x), Q(x) and v(x)?

A: The given differential equation is,

Q: Evaluate the following integrals (a) x^5dx (b)(5^2+x^10)dx (c) (12x^5+12x^3-7)dx (d) (x^3-7-(3/x^4))...

A: You have asked a question with multiple sub parts. I will address the first three of them. Please po...

Q: y = t(lnt)2 Find the derivative

A: According to the chain rule of derivative,Using the above rule, where u = t and v = ln t

Q: 2,3,4

A: (2) Evaluate the limit as follows.Substitute x = 2 and y = 3 in the given expression.

Q: Evaluate the following integral.

A: The given integral is,

Q: Suppose that the cost funtion for a commodity is  C(x)= 300+6x+1/20x^2 dollars (a) Find the marginal...

A: The given Cost function for a commodity is C(x) = 300 + 6x + (1/20)x2.(a) To find the marginal cost ...

Q: Need help solving the equation that is attached

A: x->4^+ means x is slightly greater than 4. That means we have to use the part when x>4 to find...

Q: find the exact length of the curve of the equation below, show all work y = ln(sec(x)), with a range...

A: First, we find the dy/dx

Q: Please help me find the length of the curve

A: We\'ll use arc length formula with a=pi/2, b=2pi/3.

Q: Assume a person invests $12000 at the end of each year for 30 years at an annual interest rate of r....

A: Part (a)The future value amount should be equal to A = $ 1,000,000.Please see the white board.The mi...

Q: Which of the following is the power series representation for g(x)? +8 OA. B. k 8 1 k 0 k 0 8k O C. ...

A: Note that the function g(x) is not provided (here option (c) can also be a power series). So, we are...

Q: Does the series converge absolutely, converge conditionally, or diverge?

A: The given series is

Q: A grain silo consists of a cylindrical concrete tower surmounted by a metal hemispherical dome. The ...

A:

Q: SImplify   (h3-4h)/(h3-2h2)

A: Simplify the given expression as follows.

Q: find the derivative of f(x)= 2x^3 + 4e^3

A: Given information:The given function is  

Q: find the derivative of the question in the picture please show all work

A: Obtain the derivative of the function.

Q: How can I get the result? Which is the result?

A: We have to find following limits.Question is given below:

Q: Use the shell method to find the volume of the solid generated by revolving the region bounded by th...

A: (d) First draw the graph of y = x + 6 and y = x2.Find the intersection points as,

Q: The area of a circle increases at a rate of 3 cm^2 per second. Find a) how fast is the radius changi...

A: Given information:The area of a circle increases at a rate of 3 cm square per second

Q: Product Radius (inches) Height (inches) Volume (cubic inches) Baking power 1.25 3.65 ...

A: Assuming all the items are in cylindrical shape. Look for the coffee can: The volume V is 62.12 in3;...

Q: Is y=e2x +4x+3 a solution to the differential equation shown below? y′−2y=−8x−2

A: To test if the given function is a solution of the given differential equation

Q: You must get from a point P on the straight shore of a lake to a stranded swimmer who is 60 meters f...

A: Let, "u" be the velocity at which you can swim and "v" be the velocity at which you can run.u = 2 m ...

Q: The rectangular coordinates of a point are given. Find polar coordinates of the point such that r 0 ...

A: We'll use the rectangular coordinate to the polar coordinate formula with x=-5 and y=5

Q: Use the table feature of a graphing calculator to predict the limit. Check your work by using either...

A: Step 1: Go to "Y=", then type in the function 3 + x − x2   Step 2: Go to "TBL SET" (2nd+WINDOW), the...

Q: a. Find all points on the graph of f at which the tangent line is horizontal. b. Find all points on ...

A: We first find the slope of f(x) using differentiation.

Q: Find the relative maxima, relative minima, and points of inflection, and sketch the graph of the fun...

A: Please see the white board for derivative of y, expressed as y'

Q: Find the area of the following region, expressing your result in terms of the positive integer n 2 2...

A: Obtain the limits of the integral by equating the functions as follows.

Q: Please help.

A: The given series is,

Q: Please show as much steps as possible as I am doing my best to fully understand how to solve these t...

A: Given function is, 

Q: Use​l'Hôpital'sRule to find the following limit.

A: To use L'Hopital's rule we try to get 0/0 form or infinity/infinity form first. We write x^2*cotx as...

Q: Fourier's Law of heat transfer​ (or heat​ conduction) states that the heat flow vector F at a point ...

A: Given that,

Q: Given f(x) = x^5 + x^3 - 4 , find the derivative of f inverse at the point (-2,1).

A: We are given a function as 

Q: Please help. Does the series below converge or diverge? Give a reason for your answer. (When checkin...

A: The given series is

Q: Let R be the region bounded by the following curves. Find the volume of the solid generated when R i...

A: The given curves are y=x, y=4x, y=16.The graph of the region formed by these curves is,

Q: Is y=ex −5x−8 a solution to the initial value problem shown below? y′−5x=3+y y(0)=−7

A: The given differential equation is y=ex −5x−8.The solution of the deferential equation is given as, ...

Q: Find a formula for the general term an (not the partial sum) of the infinite series (starting with a...

A: Given infinite series is, 

Q: Please help

A: Since f(x0,y0) is minimum of f(x,y). Then g(0) is minimum of g(t). That means g(0)<g(t) for t any...

Q: Find the derivative of y with respect to x

A: we are given an inverse function 

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.