A:= {(x, y) € R² :1< log(x) < 2}. = {(x, y, z) E R³: sin(xy² + «/2) · cos(z) = 1} . (a) Decide whether A and B are open, closed, both open and closed, or neither open nor closed: (b) Are A and/or B bounded? Are they compact?

Q: 1. Show that c(t) = (e¬t cos t, e-t sin t), 0 <t <∞ has finite length and calculate its valu

A:

Q: (2) Let F(x, y) = (cos(y)+2x, -x sin y+1). Show that F is path independent by finding %3D a…

A: For the given vector function to be independent, it must be derived from a potential scalar function…

Q: That the value of the integration g(1) = 0, g(2) = 0 1-e) -dt where g is a function that is…

A:

Q: tinuous at t= 0, it is continuous at every other point. 3 If the autocorrelation function R(t) of a…

A:

Q: According to numerical methods, the integral of a function f(x) over the limits a and b can be…

A: Given data  Used Simpsons 1/3 rule  f(x)=7e^(-πx)(sin(x^2)) With a=0 and b=2 and number of intervals…

Q: 1. At z = 0, the function f(z) = z ez has O a. A non-isolated singularity O b. An essential…

A: The function f(z) = ze^1/z has the only singular point at z=0 .  We will use the Laurent series of…

Q: b) Show that the “energy function" E(x, y) = 5 + is non-increasing along the solution, i.e., using…

A: (b) The objective is to show that the energy function  is non increasing along the solution, that…

Q: 4. (a) (b) Approximate the integral f x² cos xdx with n = 6 using the composite trapezoid rule;…

A:

Q: 3.) Let set S = {x, e*, sin x, cos x} be a solution to a 4th-order homogeneous differential…

A:

Q: The curved surface of a rod of length L is perfectly insulated against the flow of heat. The rod…

A: .

Q: 3. Find the total differential of z = f(x, y) if z2 - y = (1– 2x)z.

A: Total differential of a function z=fx,y is dz=∂z∂xdx+∂z∂ydy

Q: If f : [0,2] → R is defined by f(x) = 1 if 0 ≤ x ≤ 1, f(x) = 2 if 1 < x ≤ 2. Show that f is…

A:

Q: mcory amu LAampIOS 45. Finding an upper limit of an iterated integral Solve for a: 1-x² ¢4-x²-y 4 dz…

A:

Q: 2. Show that if zo is an isolated singularity of f(z) that is not remov- able, then zo is an…

A: We have to show if z0 is an isolated singularity of f(z) that is not removable, then z0 is an…

Q: 3.) Let set S = {x, e*,sin x , cos x} be a solution to a 4th-order homogeneous differential…

A:

Q: 5) (a) Show that F = (8-14xy2 + 2ye²x) + (e²x - 14x²y) y is conservative. (b) Find a potential…

A:

Q: {[{ ال 1: تحق ق من دالة التالية تحق ق معادلة لابلاس :س Z = In /x2 + y² اضف ملف ك 3. fxy ل لدالة :…

A: To find  Partial derivatives of the given functions

Q: Since f(x, y) = 1 + y² and ðf/ðy = 2y are continuous everywhere, the region R in Theorem 1.2.1 can…

A: Given data: We are given that y=tan(x+c) is the family of the solution using initial value y(0)=0

Q: 4. Is y' = sin (ty) separable a) not separable c) separable %3D b) for y =, yes d) with a proper…

A: We have to check whether the given differential equation is variable separable or not.

Q: There are continuous functions p and q such that vi(t) = t lnt, 2(t) = t2 form a fundamental set of…

A: no this is false because these can not satisfied the given differential equation

Q: Use Laplace transform to solve the partial differential equation: 8² y dy dx² at +xt where y(x,0) =…

A: Solution

Q: -) A) Find by using chain rule if f = ( , u = -1,x=-1 dx u+1 B) Evaluate the following integral:…

A: This question is based on chain rule differentiation and indefinite integral.

Q: 8 Evaluate the integral dx using the two-point Gaussian quadrature rule. 16+z1 -2

A:

Q: Use at least two methods to prove that dr/dt=0 when r=√x2 + y2, x=α cos t, and y=α sin t if α is a…

A: First method   r=x2+y2r=(α cost)2+α sint2            since x=α cost and y=α sint  =α2cos2t+α2sin2t…

Q: Xn Xn=3-(-1)" xn = cos (¹₂) √1+n² Xn= 27-5 Xn=¹ where (yn) is bounded 4 lim inf(x) lim sup(x₂)

A: We know the fct that for every  bounded  sequence  limsup(xn) and  liminf(xn) exists finitely. since…

Q: Show that the Dirichlet function f defined on [0 , 1] by f(x) = { 1 if x is rational 0 if x is…

A:

Q: Consider , xe¬**dx. What will be the appropriate solution and answer to this improper integral? A.…

A:

Q: (b) Show that the roots of y'(x) = 0 are x = 0, x = L, and x = L/2, so it follows (why?) that the…

A:

Q: [1] Show that the functions In x, In(x) are linearly dependent on (0, co)..

A:

Q: - Find the total differential df of f (x, y) = (x² + y²) 3/2.

A:

Q: - Using Greens date $(x2 + y)dx bounding of the 0<x<1 and x' sysx.

A:

Q: 3.12 Еxpress lim n00 n k3D cos 1+ as an integral. (Be sure to include the lower and upper limits|of…

A: Given: limn→∞ 2n∑k=1ncos1+2kn To convert this into the integral , use the following method

Q: Let y₁(x) and y₂(x) be any two twice differentiable functions, not necessarily eigenfunctions, in an…

A:

Q: A) If w = 2 y et* – In z where x = In(t² + 1), | dw y = tan-1 3t and z= e3t. Find by Chain Rule dt

A:

Q: 1. Find an antiderivative of f(x) = 16–x². Then, use The Fundamental Theorem of Calculus %3D 4 to…

A: Given : fx = 16-x2

Q: 14. Give the linear near-minimax approximation for f (x) = sin a on [–1, 1].

A: To determine linear near-minimax approximation for fx=sinx on -1,1 Let the approximation be px=a+bx…

Q: д. L. = a(x, y)+b(x, y) +c(x, y). – d(x, y) -

A: Proof: Consider V be any vector space of all functions of two variable x  and y whose partial…

Q: show that f(z)=(z-1) cos(1/z+2) has an essential singularity at z=-2

A: Introduction: Laurent series has an important role in determining the singularities. Suppose, a…

Q: |1) Use a sine expansion to compute the solution of ( ди д'и at ôx? u(0,t)=u(1,t) = 0,t > 0, u(x,0)…

A: According to the given information, it is required to compute the solution of the given equations.

Q: Consider the IVP S2(t) = -1+cos(t + x(t)) cos(t + x(t)) x(0) = 0. Show that the ODE is exact and…

A:

Q: Show that the p.d.f. of Z is given by g1(r) = e-1(+A)cosh(vAx), x > 0, where cosh(2) = }(e² +e=*) is…

A: Note: Hi there! Thank you for posting the question. As you have posted multiple questions, as per…

Q: b- Use Chain Rule to compute w = 2y e* - Inz } əw at x = ln(t² + 1), at (t) equal to (1) for: y =…

A:

Q: 19. Consider the integral f√x²+25 dx. 9x² a. In/√x² + 25 +x/- - b. x+ In/√x² + 25/+ √x²+25 9x √x²+25…

A: Solve the integral  √(x2+25)/9x2

Q: 1. Evaluate the integral 2 8x cos y dy dx y – 4 by reversing the order of integration.

A:

Q: Consider a zero mean stationary Gaussian process X(t) with autocorrelation function Rx (t). Find the…

A: Introduction - Autocorrelation - It is a mathematical representation of the degree of similarity…

Q: Show complete solution Expand, that is, perform the indicated operations on the differential…

A: To expand, that is, to perform the indicated operations on the differential operator, xDD+x