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    Calculus and Analysis

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    Function Calculation Process

    See attached file for full problem description. Find a function f(x) = x^k and a function g such that f(g(x)) = h(x) = sqrt(3x+ x^2)

    Average Rate of Change Problem

    A car is moving from left to right along a road which lies along the straight line 3x + 4y = 12 in the xy-plane. (The x and y coordinates are measured in miles.) The following short table gives the x-coordinate of the car at several times: t 3:00pm 3:10pm 3:15pm 3:30pm 4:00pm x -28 -24

    Paraboloid of revolution

    (Parabaloid of revolution) Determine the shape assumed by the surface of a liquid being spun in a circular bowl at constant angular velocity, W. Hint: consider a particle of liquid located at (x, y) on the surface of the liquid. The forces acting on the particle are m*W^2*x in the x direction and -m*g in the y direction.

    Differential Equations

    1. A tank with a capacity of 500 gal. originally contains 200 gal. of water with 100 lb. of salt in solution. Water containing 1 lb. of salt per gallon is entering at the rate of 3 gal./min. and the mixture flows out at a rate of 2 gal./min. (i) Write a differential equation for the concentration in the tank before the tank o

    Tangent line

    Finding tangent line for f(x) that pass through the given point ( and the point isn't on the curve) part 1 f(X) = 4x-x^2; (2,5) Part 2 f(x) =x^2; (1,-3)

    Differential Equations : Chain Falling off a Table

    A 24 foot chain, weighing Y lbs/foot of length, is stretched out on a very tall frictionless table with 6 feet hanging over the edge of the table. If the chain is released from rest , in the configuration described above, find the following: a) How long before the chain falls off the table? b) What is the velocity of the cha

    Business Calculus

    Find the present value and future value of an income stream of $1000 a year, for a period of 5 years, if the interest rate is 8%

    There is a vat of wine with a tap at the bottom

    There is a vat of wine with a tap at the bottom and a water faucet at the top. The tap is open and draining wine at a certain rate. The water faucet is adding water at the same rate, keeping the volume the same. How do I determine the concentration of the wine for any moment?

    Determine concentration of wine watered in a vat - There is a vat of wine with a tap at the bottom and a water faucet at the top. The tap is open and draining wine at a certain rate. The water faucet is adding water at the same rate, keeping the volume the same. How do I determine the concentration of the wine for any moment?

    There is a vat of wine with a tap at the bottom and a water faucet at the top. The tap is open and draining wine at a certain rate. The water faucet is adding water at the same rate, keeping the volume the same. How do I determine the concentration of the wine for any moment?

    Radius of Convergence Found

    Find the radius of convergence of About x= (-1/3) Thanks! Please see the attached file for the fully formatted problem.

    Solving Differential Equations by Separation of Variables

    Consider a right cylinderical hot tub. Radius = 5 feet; Height = 4 feet; placed on one of its circular ends. water is draining from the tub through a circular hole in the base of the tub 5/8inches in diameter. k = .6; using Torricelli's Law v = [2*g*h(t)]^1/2 and the equation dV/dt = -kAv where A is the are

    Find value of b - integral

    (See attached file for full problem description) --- If - ∫3b 3x2 dx = 37 Then find the value of b. Note - The b is supposed to be directly over the 3.

    Lennard-Jones Potentials

    The Lennard-Jones potential for the interaction of two molecules separated by distance R is U(R)= A/R^12 - B/R^6 where A and B are constants. the equilibrium separation Re is that value of R at which u(R) is a minimum and the binding energy is De = -U(Re). Express: (a) A and B in terms of Re and De. (b) U(R) in terms of R,

    Differential Equations with Variation of Parameters

    Determine the particular solution of the following nonhomogeneous differential equation using the method of variation of parameters y" + 4y' + 4y = x^-2 e^-2x ; x>0 homogeneous equation is y =C1e^-2x +C2xe^-2x y= u1e^-2x +u2xe^-2x after differentiating and letting u'1e^-2x +u'2xe^-2x =0, we have _2u'e^-2x -2'u2xe^-2

    Monthly payment calculus question

    A $100,000 mortgage is to be paid over 15 years at 7.4% per annum, compounded semi-annually, with monthly payments. What are the monthly payments (to the nearest dollar)?

    First order differential equations-mixing problem

    Consider two tanks, labeled Tank A and Tank B. Tank A contains 100 gallons of solution in which is dissolved 20 lbs of salt. Tank B contains 200 gallons of solution in which is dissolved 40 lbs of salt. Pure water flows into tank A at a rate of 5 gal/s. There is a drain at the bottom of tank A. The solution leaves tank A via thi

    Length of graph

    Please show me how to calculate the length of a curve. See attached file for full problem description.

    Finding limits using Squeeze theorem and L' Hospital theorem

    1. Compute the following limit: lim (x->2) [sqrt(6-x) - 2]/[sqrt(3-x) - 1] 2. Prove using the squeeze theorem lim (x->0) x^4 cos(2/x ) = 0 3. Show by means of an example that lim x-> a (f(x) + g(x)) may exist even though neither lim x-> a f(x) nor l

    Differential Equations : Variation of Parameters

    Determine the particular solution for the following nonhomogeneous differential equation using the method of variation of parameters Y" + y =tan(x); 0< x < pi/2 I got characteristic equation as y = U1 sin(x) + U2 cos (x) I was able to get thru to set the original D.E. to u'1 (x) cos (x) - u'2 (x) sin (x) = tan (x)

    Finding the Equation of a Line

    Find an equation of the line (in slope-intercept form) that passes through the points and sketch the graph of the equation. 1)(2,-1),(4,-1) 2)(-1,0),(6,2) write equations of the lines through the point parallel to the given line and perpendicular to the given line. 1)point:(3,-2) line:5x-4y=8 2)point:(-6,2) line:x=4

    fraction of U-238 present when the Earth was formed

    The relative decay rate of naturally occurring uranium U-238 was given in Example 4. Scientists estimate the age of the earth to be about 4.55 billion yr. Determine the fraction of the U-238 present when the earth was formed that is still present as U-238. EXAMPLE 4: A 1-G sample of pure uranium produces about 740,000 de