We are studying an inner product spaces. See attached file for full problem description. Let V be a C-space of all complex valued polynomials with an inner product.... (i) Let p be a polynomial and let Mp: V-> V be a linear operator that is given by Mp (q) :=p⋅q. Show that operator Mp has an adjoint and find it. (i
Q: The curve y = sqrt(9-x^2), -1<=x<=1 is an arc of the circle x^2 + y^2 = 9. Find the area of the surface obtained by rotating this arc about the x-axis. Note: The surface is a portion of a sphere with radius 2. See Word attachment for cleaner version with equations using Math script.
Use residue theorem to evaluate the attached.
Evaluate the integral: (sqrt(x) + 4)^3 / 3(sqrt(x)) dx
Integral with log function. See attached file for full problem description.
Approximate the integral by: a) first applying Simpson's Rule b) then applying the trapezoidal rule See attached file for full problem description.
1.) Find the interval of convergence of the series Σ (for n=0 to ∞) (4x-3)^(3n)/8^n and, within this interval, the sum of the series as a function of x. 2.) Determine all values for which the series Σ (for n=1 to ∞) (2^n(sin^n(x))/n^2 converges. 3.) Find the interval of convergence of the series Σ
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Let f be the following function with domain C = [0, 1] X [0, 1] (in two-dimensional Cartesian space): f(x, y) = 0 on the line segments x = 0, y = 0, and x = y f(x, y) = -1/(x^2) if 0 < y < x <= 1 f(x, y) = 1/(y^2) if 0 < x < y <= 1 Compute each iterated Riemann integral of f on C (by integrating first over x and then
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Show that the two integrals, E (attached) are equal.
Define the following functions on the closed interval [-1, 1]: β(x) = { 0, for x<0 ½, for x=0 1, for x>0 Let f:[-1,1] R such that f is bounded. Show that f is Riemann Stieltjes integrable with res
Suppose that f^2 is Riemann-Stieltjes Integrable. Is f Riemann-Stieltjes Integrable as well? Explain.
What is the indefinite integral for f(x) = e^x + x + 1? What is the indefinite integral of y = x^0.5? What is the definite integral for f(x) = x^3 from x = 1 to x = 2? What is the definite integral of y = xe(x^2) from x = 0 to x = 1?
What is the absolute minimum for f(x) = x^4 - 4x3 - 5?
1.) Show that the functions f1(x)=5^x, f2(x)=5^(x-3), ans f3(x)=5^x + 3^x all grow at the same rate as x approaches infinity. 2.) Determine whether each integral converges or diverges. a.) integral from 0 to 2 of (dx)/(4 - x^2) b.) integral from 0 to infinity of (5 + cosx) e^(-x)dx c.) integral from 0 to in
I am having problems understanding how to solve linear equations. For example, dy/dt = -4y + 3e^-t Can you solve this step-by-step so that maybe I can understand how to do it myself?
1.) For the arithmetic sequence {-10,-2,6,14,}, find: a.) a recursive rule for the nth term b.) an explicit rule for the nth term 2.) For the geometric sequence {512,256,128,64,...}, find: a.) a recursive rule for the nth term b.) an explicit rule for the nth term 3.) Determine whether each of the follo
1. First find a general solution of the differential equation .... then find a particular solution that satisfies the initial condition that y(1) = 4. 2. Solve the initial value problem .... 3. Nyobia had a population of 3 million in 1985. Assume that this country's population is growing continuously at a 5% annual rate and
Please see the attached file for full problem description in proper format. Question: Integral (sin theta)/(sqrt(R^2 + z^2 - 2Rzcos(theta)))d(theta)
1. Find the curl of the vector field F at the indicated point: 2. Evaluate the following line integral using the Fundamental theorem of line Integrals: 3. Use Green's Theorem to calculate the work done by the force F in moving a particle around the closed path C: 4. Find the area of the surface over the part of the
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Find the volume of the solid bounded by x = 0, y = 0, z = 0 and x + 2y + 3z = 6 by triple integration. keywords: integration, integrates, integrals, integrating, double, triple, multiple
(R,B,λ) denote the real line with Lebesgue measure defined on the Borel subsets of R. And 1≤p<∞ 1. Show that the sequence fn = n χ[1/n, 2/n] (χ is a step function) has property that if δ>0, then it is uniformly convergent on the complement of the set [0,δ]. However, show that there does
Concern the region bounded by: y=x^2 y=1 and the y axis find the volume of the solid obtained by rotating the region around the y-axis
Find the area: a) between the curves y = 11/(x^2) and y = 12 - x^2 b) between the curves y = x/3 and y = x^4
Compute the following integrals a. integral x(x^4 - (x^2 + 2 / x))dx b. integral ((x^5/3 - 3x^1/5)/x^3/4)dx c. integral tan^5 x sex^3 x dx d. integral (6x + 4x^3)(1 + 3x^2 + x^4)^3 dx
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Evaluate the integral sec^4 theta tan^4 theta dtheta with a lower limit of 0 and an upper limit of pi/4
Evaluate the integral. sin^6 x cos^3 x dx