Let P(z) be polynomial of degree n and let R>0 be sufficiently large so that p never vanishes in { z: |z| >= R}. If gamma(t) = Re^(it), 0 =< t =< 2 pi, show that the integral over gamma p'(z)/p(z) dz = 2 ( pi ) i n.
(a) If f is a nonnegative continuous function on [0,1], then show that integral from 0 to 1 f(x) dx = integral over [0,1] f dx ( that is show that the reimann integral and lebesgue integrals are equal). (b) Prove part (a) for any continuous function.
The problem is the integral of ( (w - 3)^1/2 ) / ( 2 + (w-3)^1/2 ) so its the root of (w-3) divided by the root (w-3) + 2.
(See attached file for full problem description).
(See attached file for full problem description with proper equations) --- 1. For medical purposes the level of sugar was measured in blood (in mg/dl). The samples were taken with 1/2 hour increments, as the following table shows: Initial sample 96 mg/dl After 30 min. 133 mg/dl After 60 min. 142 mg/dl After 90 min.
In a previous problem I posted here: Let f(x) be a positive continuous function on [0,1/2], f(x) =< 1/2. Let A = { (x,y) : 0 =< x = 1/2, 0=<y=< f(x)} Prove that; m*(A) = integral from 0 to 1/2 of f(x)dx. Now knowing that the above is true, I want to show that the integral is lebesgue measurable, that is, the area un
Let X be an uncountable set, let m be the collection of all sets E in X such that either E or E^c is at most countable, and define M(E) = 0 in the first case, and M(E) = 1 in the second case. ( m here is sigma algebra in X). The Questions is : Describe the integrals of the corresponding measurable functions.
1) the indefinite integral of du/(u(a+bu))=(1/a) ln |u/(a+bu)| + c in words the indefinite integral of du over the quantity of u times the quantity of a plus b times u... 2) the indefinite integral of du/(u((a+bu)^2))= 1/(a(a+bu))= 1/(a^2) ln | (a+bu)/u| +c the indefinite integral of du over the quantity of u times t
1) The integral of dx divided by the the quantity of e^-x+1 also known as the indefinite integral of dx/((e^-x)+1) 2) Solve the indefinite integral of the quantity of 1 minus e^x all over the quantity of 1 plus e^x with respect to x... also know as the indefinite integral of (1-e^x)/(1+e^x) dx
1) Indefinite integral of dx / ((x^2)(sqrt[a^2-x^2])) with respects to x In words it is the integral of the derivative of x all over the quantity of x squared times the square root of a squared minus x squared 2) Indefinite integral of dx / ((e^x)(sqrt[4+e^2x])) with respects to x in words it is the integral of the der
Please help on how to work out the solution to a function using the 'D-contour' (see attached file).
(See attached file for full problem description with proper symbols). --- Let and for (a) Use integration by parts to show that in for . Deduce that for (b) Compute for and verify that.
1).If A is a subset of B, A,B in m ( measurable sets) then show that integral (region A) s dM =< integral ( region B) s dM Where s here is a simple non-negative measurable function. ( Please don't confuse this with bounded measurable functions, I need the proof for SIMPLE functions). 2). If E are measurable, X_E is the c
An oil company discovered an oil reserve of 100 million barrels. For time t>0, in years, the company's extraction plan is a linear declining function of time as follows: q(t)=a-bt Where q(t) is the rate of extraction of oil in millions of barrels per year a time t and b= 0.1 and a =10 . a) How long does it take to exhaust
36)After t weeks, contributions in response to a local fund raising campaign were coming in at a rate of 2000te^-0.2t dollars/week. How much money was raised during the first five weeks. 38) Find the volume of the solid generated when the region under the curve y=sinx+cosx on the interval [0,pi/4] is revolved about the y axi
Find the area of each polar region enclosed by f(theta) for a <=theta<=b 36) f(theta) = theta/pi, 0<=theta<=2pi PLEASE SHOW EVERY STEP IN SOLVING THESE-NO COMPUTER PROGRAMS PLEASE. 4) Identify each curve as cardiode, rose(state # of petals), leminscate, limacon, circle, line or none of above. a) r=2sin2theta b) r^2=2c
Sketch the region bounded between the given curves and then find the area of each region for 16 and 22. 16) y=x^2+3x-5, y=-x^2+x+7 22) x axis, y=x^3-2x^2 -x+2 28) Find the area of the region that contains the origin and is bounded by the lines 2y=11-x and y=7x+13 and the curve y=x^2-5. Please see the attached file f
4. The demand curve for a product has equation p=20 e^(-0.002q) and the supply curve has equation p=0.02q + 1, where q is the quantity and p is the price in $/unit. a) Which is higher the price at which 300 units are supplied or the price at which 300 units are demanded? Find both prices. b) Sketch the supply and deman
6. The demand curve for a product has equation p = 100 e^(-0.008q) and the supply curve has equation p = (4√q) + 10 , where q is the quantity and p is the price in dollars/unit. a) At a price of $50, what quantity are consumers willing to buy and what quantity are producers willing to supply? Will the market push price
Calculate integral using Gauss theorem. See attached file for full problem description.
A service station orders a 100 cases of motor oil every 6 months. The number of cases of oil remaining t months after the order arrives is modeled by f(t) = 100e^(-0.5t) a) How many cases are there at the start of the six-month period? How many cases are left after the end of the six-month period? b) Find the average number
Evalutate the following: 1.) Integrate sech ^2x/ (2+ tanh x) dx 2.) Integrate from 0 to (Pi/2) sinx/(1+cos^2 x) dx 3.) Find (f^-1)' (a) of f(x)=x^5 - x^3+ 2x, a=2 4.) Find the limit x approaches (2-) e^(3/(2-x))
Use the convolution integral method and hand calculation to come up with the exact formula for the solution of y'' [t] + 5y' [t] +6y[t]= 3.8E^(-t) with y [0]=2 y' [0]= -1
I need help with the TI-83. I dont want the problem solved, just need to be walked through the steps for inputting data into the TI-83 to mimic the graph as shown in the document. I have tried many ways and I keep getting the wrong graph. Thank You. a) Graph x3 - 5x2 + 4x , marking x = 1,2,3,4,5 b) Use th
The marginal cost function of producing q mountain bikes is a) If the fixed cost in producing the bicycles is $2000, find the total cost to produce 30 bicycles b) If the bikes are sold for $200 each, what is the profit (or loss) on the first 30 bicycles c) Find the marginal profit on the 31st bicycle. Please see the atta
A) Graph , marking x = 1,2,3,4,5 b) Use the graph and the area of interpretation of the definite integral to decide which of the five numbers for n = 1,2,3,4,5 is largest. Which is smallest? How many of the numbers are positive? (Do not calculate integrals). (See attached file for full problem description)
#22) Find the moment of inertia of a lamina S of density 1 about an axis A, where S: x2+ y2=1, A: the line z= h/2 in the xz-plane (See attached file for full problem description with equations) --- Question in Kreyszig's Advanced engineering mathmatics 8th ed.: section 9.6: Surface integrals
#16) Surface integrals; s G(r) dA. Evaluate these integrals for the given data. (show the details.) G=(x2+ y2)2 - z2, S: r=[u cos v, u sin v, 2u], 0 u 1, -  v   (See attached file for full problem description with equations) --- Kreyszig's Advanced e
#12) Surface integrals; s G(r) dA. Evaluate these integrals for the given data. (show the details.) G=cosx + siny, S: the portion of x+y+z=1 in the first octant (See attached file for full problem description with equations) Question in Kreyszig's Advanced engineering mathmatics 8th ed.: section 9.
(See attached file for full problem description with equations and diagram) --- Compute ∫r+ (bar-z + z^2 bar-z) dz where gamma+ is a square with side = 4, centered at the origin and traced counterclockwise once ---