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# Calculus and Analysis

See attached

### Limits

See attached 1) F(x) = Is this continuous at x = 3?

### Particular solution of a differential.

If dy/dx = 2y^2 and if y = -1 when x = 1, then when x = 2, y = ?

### Differential Equations : Free Fall and Terminal Velocity

An object in free fall in a gravitational field is governed by the ODE m*dv/dt=mg + Fs, where m is the mass of the object, g=9.8 meters/sec is the acceleration of gravity, v(t) is the velocity of the object t seconds after it is released, and Fs denotes external forces acting on the object. In all that follows, assume that v(0)

### Area of the Surface from Intersection of Two Cylinders

#22 Please see the attached file for full problem description.

### Chaos : Conjugacy in Discrete Dynamical Systems

I am taking a course in Dynamics/Chaos and I am trying to prove conjugacy between the logistic and quadratic functions. I have some ideas, but cannot get the proof to work. Attached is a word document with the functions and problem.

### Reflection a graph about the origin

The graph of y=x^3 for x>=0 is given below. Complete the graph for x<0.

### Evaluating a simple limit

Evaluate Lt [(x2+5x+6)/(2x2-3x)] x&#8594;2

### Slope of a curve

Find the slope of the curve at point A in the graph.

### Estimating Limit of a function from Graphs and Tables of data

Let y=f(x)=x^2+3 Find Limit of f(x) as x approaches 2 using both graph and table

### Intermediate value theorem: Definition, Illustration by Graph and its application

Define Intermediate-Value theorem Using this theorem, show that there is a root of P(x)=x^3+x^2+x-1 in the closed interval [0,1].

### Discontinuous function

Define a discontinuous function and state the conditions for discontinuity. Find whether the following functions are discontinuous: f(x)=1/x and f(x)=(x)^(1/2) Solve the following:(involves jump discontinuity) A tomato wholesaler finds that the price of newly harvested tomatoes is \$16 per pound if he purchases fewer th

Find the radius of convergence of the series in the attached file 'Series.doc'.

### Finding tangent through a certain point (involves drawing a diagram)

A portion of a river has the shape of the equation y=1-x^2/4, where distances are measured in tens of kilometres, and the positive y-axis represents due north. the town of Coopers Crossing is situated on the river at its most northerly point. The town of Black Stump is 10 kilometres due south of Coopers Crossing. the town of And

### Recursive Equations : A 2x2xn hole in a wall is to be filled with 2n 1x1x2 bricks...

Q.A 2x2xn hole in a wall is to be filled with 2n 1x1x2 bricks. In how many ways can this be done if the bricks are indistinguishable?

### Line Equations : Tangents & Normals

I) Find the equation of the tangent to y=x(1-x) at x=1 ii) Find the equation of the normal to y=x(1-x) at x=1 iii) Find the equations of the tangents to y=x(1-x) that pass through (-1, 1/4)

### The normalization constant of a Hermite polynomial

I need to figure out how to explicitly calculate the normalization facotor for the Hermite polynomial as it relates to the harmonic oscillator. N=[(a/Pi)1/2vv!]

### Multivariable calculus

Please show all work; don't explain each step. Please DON'T submit back as an attachment.Thank you Sketch the solid bounded by the graphs of the given equation and find its volume by triple integration: z = 10 - x^2 - y^2, y = x^2, x = y^2, z = 0

### Multivariable Calculus : Centroid of a Plane

Find the centroid of the plane region bounded by the given curves. Assume that the density is &#61540; = 1 for each region: x = 0, y = 0, x + 2y = 4 &#61540;: is the density symbol

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

Find the volume of the solid that is bounded above and below by the given surfaces z = z_1(x, y) and z = z_2(x, y) and lies above the plane region R bounded by the given curve r = g(u): z = 0, z = 3 + x + y; r = 2 sin u

### Multivariable Calculus : Double Integral - Polar Coordinates

Find the indicated area by double integration in polar coordinates: The area inside both the circles r = 1 and r = 2 sin u

### 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)

### Finding The Solution For Differential Equations

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

### Differential equation

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

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 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

### 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

### Parametric Equation

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