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Calculus and Analysis

Calculus questions

1. What is missing in this surface of revolution as a function of x revolved around the y-axis: ? A) Nothing, the formula is fine as is. B) Nothing, but the limits of integration should be on the interval [c, d]. C) The variable x should be x2. D) The constant 2π is missing. 2. Find the solid of revolu

Equilibrium quantity and price

Consider a market with the following supply and demand functions: QD = a0 - a1PD a0, a1 > 0 QS = b0 + b1PS b0, b1 > 0 (a) Find the equilibrium quantity and price as a function of the parameters (use any method you like). Are there any additional restrictions that you must impose on the parameters for

Determining the Maximum Separation

The positions of two particles on the s-axis are s1=sin t and s2=sin(t+ π /3), with s1 and s2 in meters and t in seconds. a) At what time(s) in the interval 0 ≤t ≤ 2π do the particles meet? b) What is the farthest apart that the particles ever get? c) When in the interval 0 ≤t ≤ 2π is the distance between the parti

derivative of the function ..

1. Compute the derivative of the given function and find the slope of the line that is tangent to its graph for the specified value of the independent variable. (Compute the derivative of the function from the definition only, using limits. More advanced methods are not allowed here. Show your work.) (i) f(x) = x^2 - 1 x = -


Find the indicated probability. 1) Two fair dice are rolled. What is the probability that a sum of 6 or 11 is obtained? 1) _______ A) 7/6 B) 17/36 C) 1/66 D) 7/36 Find the simple interest. Assume a 360-day year. Round results to the nearest cent. 2) $ 49,417 at 7.7% for 17 months 2) _______ A) $

Calculus Review problems

I have a couple of problems I need assistance with. Please include complete explanation and work. (see attached for equations) Question 3: Consider the region R bounded by the curves y = 0, y = x-2, and y = . a). Sketch the region R. b). Set up (do not evaluate) the integral for computing the volume of the sol

Implicit differentiation and Numerical values of derivatives

Need help with calculus homework problems. In Exercises 41-48, find dy/dx 44. 5x 4/5 + 10y 6/5 = 15 ____________________________________________________________________ 54. a. By differentiating x 2 - y2 =1 implicitly, show that dy/dx = x/y b. Then show that d2y/dx2 = - 1/y3. ____________________

Accounting : Profit Margins, Turnover and Return on Investment

The Valve Division of Bendix, Inc, produces a small valve that is used by various companies as a component part in their production. Bendix, Inc., operates its divisions as autonomous units, giving its divisional managers great descretion in pricing and other decisions. Each division is expected to generate a mimimum required

Unit Ramp and Heaviside Functions : Inverse Laplace Transforms

Define the unit ramp function by ... 1. Determine the Laplace transform of H(t) 2. Use the Laplace transform to solve the ODE ..... Questions: 1. To determine the Laplace transform, do we use ..... ∫ (note the difference in integration limits). I know both integrals will give the same answer. But I am confused bec

Laplace transforms

Please help working on these problems Please show all steps section 7.6 # 6,9,12,26,36 See attached Express the given function using unit step functions and compute its Laplace transform. Determine an inverse form of the given function. Determine L(f), where the periodic function is described by its graph. Solve t

Tangent line problem

Explore the following function. You are to decide which of threee lines given are tangent to the graph of f(x) at given points. The function to define is F(x)=2x^3-4x^2+3x-5 The possible tangent lines are: y= x-5 y= 2x-5 y= 3x-5 a) what is/are the zero(es) for this function? In other words, what is the solu

Explain L'Hopital's Rule and How to Apply It

I can't seem to grasp the concept of L'Hopital's Rule. How do you know whether to use it or not in evaluating a limit? If anyone could answer this and give me a step by step example for how to solve this that would be extremely helpful (the more complicated the example, the better, since the examples on our tests will be very

Legendre's Differential Equation

The attached file has all the information about this problem. I have updated the information. Truly I DON'T UNDERSTAND WHAT THE PROFESSOR HAS ASKED FOR? THAT IS WHY I NEED HELP. BELOW IS WHAT HE ASKED IN ADDITION TO MY PREVIOUS ANSWER. On this problem, we know from a previous problem that the Legendre polynomials satisfy

Sales growth

Attached SALES GROWTH: The rate of change in sales S (in thousands of units) of a new product is proportional to the product of S and L - S. L (in thousands of units) is the estimated maximum level of sales, and S = 10 when t = 0. Write and solve the differential equation for this sales model.

Differential Equation

Attached Match the solution of the differential equation in the text to the following differential equation: Differential equation in text = y' + P(x)y = Q(x) (standard form) NOTE: 1) write the equation in standard form 2) find the integrating factor: u(x) = e^(ʃP(x)dx) 3) evaluate the integral to find the

Verify the solution

Attached Verify that the function is a solution of the differential equation: Y = Ce^-t + 10 y^1 + y - 10 = 0

Fundamental Theorem of Calculus

See attachment Use Part I of the fundamental theorem of calculus to find the derivative of the function... The velocity graph of an accelerating car is shown... Find the interval on which the concave upward

Differential equations.

(1)find the general solution of x^2y" - xy'+ y = x^2, x > 0 (2)the initial value problem of y"'+y' = 2 + sin(x), y(0)=0,y'(0)=1, y"(0)=-1.