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# Calculus and Analysis

### How do I solve this problem of second - degree equations?

Sketch the graphs of each pair of circles to determine the number of points of intersection. If the circles are tangent or fail to intersect, say so. Then solve the system. 2 2 2 2 x + y - 4y= 0, x = y - 2x = 4 How do I go about solving?

### Normal Modes : Second Order Simultaneous Equations

This question is concerned with finding the solutions of the second order simultaneous equations where a = 38, b = -9, c = 378, d = -79 (i) Find the particular solutions to the differential equations which satisfy the initial conditions x = -10 and y = 7 at t = 0 together with the condition at t = 0.. For this part

### Heat Equation : Moving Source - Dirac Impulse Function

Please see the attached file for the fully formatted problem. Use superposition to solve: with boundary conditions: and initial condition

### Prove Using the Chain Rule

Please see the attached file for the fully formatted problems. Let x,y denote Cartesian coordinates and denote polar coordinates, and let . Using the chain rule show that (you may assume that ). Hence show that

### Rate of Change of Volume Given Rate of Change of Height

The height h of a right circular cone is 20 cm and is decreasing at the rate of 4 cm/sec. At the same time, the radius r is 10 cm and is increasing at the rate of 2 cm/sec. What is the rate of change of the volume in cm3/sec? (Note: The volume of a right circular cone is V = 1/3p r^2h.)

### Find the Limit of Equation

Please see the attached file for the fully formatted problem. If lim x --> 0 f(x) = 3 then lim x--> 0 (e^(2x)-1)/(x f(x)) = ?

### Find the Limit : L'Hopital's Rule

Please use L'hopital's Rule to find the limit of the following expression Lim x-->0 (xsin(2x))/(1-cos(x))

### Find the Limit : L'Hopital's Rule

Lim n-->&#8734; 2^(-n) ln n

### Heat Diffusion Equation and Standard Heat Equation

A) Let the temperature u inside a solid sphere be a function only of radial distance r from the center and time t. Show that the equation for heat diffusion is now: {see attachment}. This is not an exercise in doing a polar coordinate transformation. First you should derive an integral form for the equation by integrating over a

Given the following table...(a) Is y a function of x? Explain your answer. (b)Is x a function of y? Explain your answer. (See attachment for full question) Hi, I am having trouble doing these problems listed below. Please show me how to solve these problems for future reference. Thank you very much. I would like for you

### The problems are from Boundary Value Problems

The problems are from Boundary Value Problems. Undergrad 400 level course. Mainly uses partial differential skills. Some problems might require using MATLAB. Please explain each step of your solutions. Thank you very much.

### The problems are from Boundary Value Problems

The problems are from Boundary Value Problems. Undergrad 400 level course. Mainly uses partial differential skills. Some problems might require using MATLAB. Please explain each step of your solutions. Thank you very much.

### Rate of Change of Height of Cone

Gravel is dumped from a conveyor belt at the rate of 30 cubic feet per minute and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and heght are always equal. How fast is the height of the pile increasing when the pile is 10 feet high? include the correct units in your answer. Let h=the heig

### Boundary Conditions for Transport Phenomena

In solving transport phenomena problems, we use "boundary conditions" and "initial conditions". In mathematical terms, (that is, types of variables), what are "boundary conditions" and what are "initial conditions"

### Non-empty bounded subset of R.... then prove a function

Pls provide step by step proof with explaination. Thanks.

### Differential Equation into Transfer Function

Transform the attached differential equation into a transfer function and find the homogeneous solution to the differential equation from the transfer function. See the attached file.

### Advanced Calculus Analysis : Cauchy and Convergent Sequences

We proved the following theorem in the class: "If a>0 and if a sequence... is covergent, then the sequence... is convergent." In proving this theorem, we proved that... is Cauchy instead of proving it converges directly. Why did we have to do that? Please see attachment for full question.

### Advanced Calculus Analysis : Simplify using Set and Interval Notation

Let f: R &#8594; R defined by f(x) = x² for all xER. Use set notations (for example, &#8745;, U, &#8722;) and interval notations to simplify the sets f(f-¹ [-1, 3]) and f-¹(f[-1, 3]).

### Advanced Calculus : Negate the Definition of a Function Being Onto

Convention: Let X and Y be non-empty sets of real numbers. Let g: X &#8594; Y be a function. 1. Negate the definition of the function g: X &#8594; Y being onto. (8 points)

### Solve the Differential Equation

Solve: ((e^x)(sin(y))-2ysin(x))dx+((e^x)(cos(y))+2cos(x))dy= 0

### Solve the Differential Equation

Solve: (cos x + lny)dx + ((x/y)+ e^y)dy = 0

### Solve the Differential Equation

(x^2 +1)y' + 3xy = 6x

### Question about Solve the Differential Equation

Question about Solve the Differential Equation (6xy-y^3)dx + (4y+3x^2-3xy^2)dy = 0

### Find the general solution to the driven differential equation.

Find the general solution to the driven differential equation attached. The solution is detailed and well presented. The solution received a rating of "5" from the student who posted the question.

### Temperature Distribution Exposed to a Hot Gas Stream

See the attached file. You solution can be similar, but IT CANNOT BE IDENTICAL OR LOOK ANYTHING CLOSE TO IDENTICAL. Please see the attached file for the fully formatted problem. L .M. Chiappetta and D.R. Sobel ("Temperature distribution within a hemisphere exposed to a hot gas stream," SIAM Review 26, 1984, p. 575?577)

### Find the Laplace Transform of a Product

Simple Laplace transform of a product of two trig identities of which I cannot remember how to integrate. See the attached file.

### Laplace Transform to Solve IVP

Use Laplace transform to solve an IVP style problem. Where y^n(t)+a^2y(t)=0 and a is not equal to zero.

### Laplace transform : Solve an Initial Value Problem

Please see the attached file for the fully formatted problem. Suppose there was an IVP such as the following: where Where and how do you begin to set this problem up to be solved using the Laplace transform? The value y(4)(t) is the fourth derivative of function y(t).

### Inverse Laplace Transforms and partial fractions

I have a transform F(s) of which I need the inverse transform for. The form of the transform is not of a common form and I am having trouble reducing it to a workable form. I am looking at a problem that requires the inverse laplace transform of f(t) to be found using the following transform: F(s) = (s*e^(-s/2))/(s^2 + p

### Laplace Equation Inside Quarter-Circle/Disk

Solve the Laplace equation inside the quarter-circle if radius {see attachment} is subject to boundary condition: {see attachment} Thank you.