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# Calculus and Analysis

### Multivariable Calculus : Volume of a Solid of Revolution

Find the volume of the given solid: The solid lies under the hyperboloid z = xy and above the triangle in the xy-plane with vertices (1, 2), (1, 4), and (5, 2)

### Multivariable Calculus : Volume of Solid of Revolution

Find the volume of the solid that lies below the surface z = f(x, y) and above the region in the xy-plane bounded by the given curves: z = 1 + x^2 + y^2; y = x, y= 2 - x^2

### Multivariable calculus

Please show all work; don't explain each step. Please DON'T submit back as an attachment.Thank you. ( &#61682; ^n_r means that n is on the top of the &#61682; and r is on the bottom) Evaluate the iterated integral : &#61682; ^1_0 &#61682; ^(x^2)_0 xy dy dx &#61682;: is the integral symbol

### Multivariable calculus

Please show all work; don't explain each step. Please DON'T submit back as an attachment.Thank you. ( &#61682; ^n_r means that n is on the top of the &#61682; and r is on the bottom) Evaluate the iterated integral: &#61682; ^2_0 &#61682; ^2x_0 (1 + y) dy dx &#61682;: is the integral symbol

### Differential Equation Question.

Find the general solution of the differential equation: y'' + 2y' + 2y = 2e^(-x) tan^2 x.

### Finding The Solution For Differential Equations

Find the general solution of the differential equation: y'' + y = tan x sec x

### Differential Equation General Solution

Find the general solution of the differential equation: y'' - 2y' + y = (e^x)/x

### Solution of Differential Equation

Verify that y_p , where y_p(x) = sin 2x, is a solution of the differential equation: y'' - y = -5 sin 2x. Use this fact to find the general solution of the equation

### Differential Equation Solution Function

Please show all work; don't explain each step. Please DON'T submit back as an attachment.Thank you. Find the general solution of the differential equation: y''' + 2y'' + y' + 2y = 0

### Differential Equations with Third Derivatives

Please find the general answer to this particular differential equation: y'''+ y'' = 0

### Finding the General Solution to a Differential Equation

Please calculate the general solution to the following differential equation: y''' - 6y'' + 12y' - 8y = 0

### Solve the Differential Equation Inside

Find the general solution of the differential equation that can be read below: y''' + 3y'' - 4y' = 0

### Finding Real and Complex Solutions to a Differential Equation

For the following differential equation find all numbers r, real and complex, such that e^(rx) is a solution; find two linearly independent real solutions: (D^2 - 3D + 2) y = 0

### Differential Equation : Basis

Verify that the given functions form a basis for the space of solutions of the given differential equation: x^2 y'' - 2xy' + 2y = 0, f_1(x) = x, f_2(x) = x^2, x > 0

### Limit Calculation

Lim (x-1)*ln(x) x->1

### General calculus

20) If the function f is continuous for all real numbers and lim as h approaches 0 of f(a+h) - f(a)/ h = 7 then which statement is true? a) f(a) = 7 b) f is differentiable at x=a. c) f is differentiable for all real numbers. d) f is increasing for x>0. e) f is increasing for all real differentiable ans is B. Explain

### Differential Equation

Most drugs are eliminated from the body according to a strict exponential decay law. Here are two problems that illustrate the process. 1. The drug Valium has a half-life in the blood of 36 hours. Assume that a 50-milligram dose of Valium is taken at time t=0. Let m(t) be the amount of drug in the blood in milligrams t hours

### Solve: Multivariate Calculus

Please see the attached file for full problem description. (a) where R is the region in the first quadrant which lies inside the circle x^2 + y^2 = 2x and outside the circle x^2 + y^2 = 1. (b) If f(x,y) = x/y and h(x,y) = (1/2)x^2 - 4y find the rate of change of f(x,y) at the point (2, -1) in the direction in which h(x,y)

### Parametric Equation Position and Range

Professional golfer Nancy Lopez hits a golf ball with a force to produce an intinial velocity of 175 feet per second at an angle of 35 degrees above the horizontial. She estimates the distance to the hole to be 225 yards. A) Write the position of the ball as a pair of parametric equations. (I know that it is x=175tcos(35)and

### Curve in polar coordinates and find the area of the inner loop.

Sketch the curve in polar coordinates given by r = 2-4 sin theta Find the area of the inner loop. Find the area of the inner loop for the general case: i.e. r = b - a sin feta (0 less than b less than a )

### Vector Problem: Force up Ramp

What would be the force required to push a 100-pound object along a ramp that is inclined 10 degrees with the horizontal?

### Maxima-Minima Problem with Two Variables

Find the maximum & minimum values over the square with vertices (0,0) (2,0) (0,2) (2,2) for the function f(x,y)=6x-x^2+2xy-y^4.

### Find the area bounded by one loop of a curve.

Find the area bounded by one loop of the curve given by x=sint, y=sin2t You should provide suitable notes to justify you solutions.

### Sketch the curve in polar coordinates given by r=2-4sin feta

4) Sketch the curve in polar coordinates given by r=2-4sin feta Find the area of the inner loop. Find the area of the inner loop for the general case: i.e. r=b-asin feta (0 isless than b is less than a)

### LAPLACE TRANSFORMS

Please see attachment. Require problems solving, also explanations etc for better understanding.

### Working with Maximum Resulting Error in Calculation of Area

Show all work. Please DON'T submit answers back to me as an attachment. The dimensions of a closed rectangular box are found by measurement to be 10 cm by 15 cm by 20 cm, but there is a possible error of 0.1 cm in each. Use differentials to estimate the maximum resulting error in computing the total surface area of the box.

### Calculus 3 and 4

Show all work. Please DON'T submit answers back to me as an attachment. Thank you. Determine whether the function is homogenous. If it is, state the degree: f(x, y)=5x^2 + 2xy

### Calculus differential equation

Find the order of the differential equation and determine whether it is linear or nonlinear: y^(4) + 3(cos x)y''' + y'=0

### Find ∫ e^(-x^2)dx by using Laplace Transform.

Laplace Transform Inverse Laplace Transform To find the value of ∫ e^(-x^2)dx by using Laplace Transform, where the range of integration is

### It is a short description for finding the higher order derivatives of the function f(x)= (2^2^x)+1.It represents a Fermat Number when x is a positive integer. Find the higher order derivative of the function f(x) = [2^(2^x)] + 1.

Differential Calculus Fermat Numbers Higher Order Derivatives of f(x) = [2^(2^x)] + 1 The function f(x) = [2^(2^x)] + 1 represents Fermat numbers when x = 1,2,3,... Find the higher order derivative of the function f(x) = [2^(2^x)] +