Problem: Given the power series for the following function (1+x)^k (a) Write the power series for (1+x)^(1/3) (b) Use the power series from part (a) to find the power series for x^3 (c) Using this series approximate the following integral (1+x^3) ^(1/3) using the first three terms
(a) Use the integral definition of the Laplace transform to compute (FUNCTION1) (b) A function g(t) has the transform (FUNCTION2). Use transform properties to compute the following. Express each in simplest form: i) (FUNCTION3) ii) (FUNCTION4) (See attachment for full question).
Find the explicit solution to the ODE 2yy'=(1+y^2) subject to y(0)=4. What is the solution if y(0)=-4? *(Please see attachment for proper citation of symbols and numbers)
Consider the vector field F=((x^2)*y+(y^3)/3)i,(i is the horizontal unit vector) and let C be the portion of the graph y=f(x) running from (x1,f(x1)) to (x2,f(x2)) (assume that x1<x2, and f takes positive values). Show that the line integral "integral(F.dr)" is equal to the polar moment of inertia of the region R lying below
Using the coordinate change u=xy, v=y/x, set up an iterated integral for the polar moment of inertia of the region bounded by the hyperbola xy=1 , the x-axis, and the two lines x=1 and x=2. Choose the order of integration which make the limits simplest THIS MESSAGE IS ADDRESSED TO ANY TA: I found something , I just want you
Consider a block diagram describing a system under proportional-integral control (as show in figure in attachment): Find the constraints and determine the range (using the Routh-Herwitz criterion) of Kp and Ki. Also, find the closed loop system transfer function assuming the controller gains are set to a specific value. (Ple
See attached explanation Differential equations are not my strong suit now. Please explain in a simple way each step from the integral 1/F dF to the final answer. Show and tell how you get from step to step. On problem 35 please answer and explain this in the simplest way you can for me to understand please. Step by
Please assist me with the attached problems relating to functions and integrals.
Prim is primitive! In genral the moment of inertia around an axis( a line) L is: Isubl=double prim (dist(.,L)^2*delta*dA) The collection of lines parallel to the y axis have the form x=a .Let I=Isub(y) be the usual moment of inertia around the y axis I= double prim of x^2*delta*dA Let I(bar) be the moment of ine
Find the average area of an inscribed triangle in the unit circle.Assume that each vertex of the triangle is equally likely to be at any point of the unit circle and that the location of one vertex does not affect the likelyhood the location of another in any way. (note that the maximum area is achieved by the equilateral trian
Compute the mass, centroid, and moments Ix, Iy and Io of the half-disk: y>0, x^2+y^2<1 with density delta(x,y)=y it is said we should know the primitive (sin(x))^n or (cos(x))^n from Pi/2 to 0
Find the integral of f(x,y)=x^2 over the domain D which is bounded by y=3x, x=3y and x+y=4 Hint: use the transformation x=3u+v and y=u+3v
Find the integral over C of f(x,y) = x^2 where C is the unit circle
A tank contains 1320 L of pure water. A solution that contains .01kg of sugar per liter enters a tank at the rate 3L/min. The solution is mixed and drains from the tank at the same rate. Find the amount of sugar after t minutes as a function of t.
Evaluate integrate (3sin2x - 2cos3x)dx a=pi/4 and b=pi/2.
Please see the attached file for the fully formatted problems.
Evaluate the attached integral: a) Write an equivalent iterated integral with the order of integration reversed. b)Evaluate this new integral and check that your answer agrees with part (a)
Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the y axis. 1. y=x. Line goes from (0,0) to to (2,2). Picture shows a thin yellow rectangle going from about x=1.5 vertical to the y=x line. 2) y=sq. root of x. Line goes from (0,0) t
Please see the attached file for full problem description. --- Find the volume of the region that lies under the graph of the paraboloid z = x^2 + y^2 + 2 and over the rectangle R = {(x, y) | -1 and in two ways (a) by using Cavalieri's principle to write the volume as an iterated integral that results from slicing
Find by the method of summation the value of: a. Integral (a - 0) sin nx dx b. Integral (1/2 pi - 1/4 pi) cosec^2x dx Please view the attachment for proper formatting.
Find by the method of summation the value of : a) The integral (from 0 to 1) of the square root of x. (dx) b) The integral (from 1 to 4) of 1 divided by the square root of x. (dx) Please view the attachment for proper formatting.
Integration as the limit of a sum (II) Find by the method of summation the value of: a) The integral (from 0 to 1/2*pi) of sin(x). b) The integral (from a to
Integration as the limit of a sum (I) Find by the method of summation the value of:-
See Attachment for equation We know that sin z and cos z are analytic functions of z in the whole z-plane, what can we conclude about *(see attachment for equations)* in the first quadrant
Find the integral by the method of summation the values of :- (a) integral of e^(-x) where the range of integration is from a to b. (b) integral of e^(kx) where the range of integration is from a to b.
I am new to Mathematica and did derive the answer to the following but I can not get the information as to the steps taken to derive it. I am using the trapezoidal and Simpson's rules to evaluate S20 x2 dx ( the S should be the variant symbol) Compare with exact value. My answer is 8/3 but I can not get Mathema
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Please see word attachment for clearer view of the problem. Volume: Find the volume of the solid generated by revolving the region bounded by the graphs of y = xe^-x, y = 0, and x = 0 about the x-axis.
Please help with various Calculus questions. You do not need to show your work for this one because I would simply like to compare your answers with mine so that I am sure that I did everything correct on mine. Please just write your exact answer after each number. I will know which problems I will have to study in detail w
Use l'hopital's rule if needed. Show all work step by step. Use proper notation please. Surface Area: The region bounded by [(x-2)^2]+y^2=1 is revolved about the y-axis to form a torus find the surface area of the torus. PLEASE show or explain step by step process.