Regular Let N be the Submodules of that quotient module M are Submodule of M. prove that of the Form U where U is submodule of 4 M Containing No

Q: 4. The two differentiable functions f(r, g) and g(r,0) satisfy the identity 9(r, 6) = S(r cose, r…

A: Given two differentiable function are f(x,y) and g(r,θ)  such that g(r,θ)=f(rcosθ,rsinθ) given that…

Q: If the roots of the equation ax²+bx +c = 0 be a and s and those of the equation b - 4ac Ax + Bx +C =…

A: Introduction :

Q: Find the circumference of a circle described by the parametric equations = 7 cos 0 and y = 7sin 0…

A: The formula L=∫dxdθ2+dydθ2dθ is formula for length of arc in polar coordinates. As we go along the…

Q: y" - 3y' = e3x – 12x %3D

A:

Q: Solve the problem. 28) A kitchen remodeling company determines that the marginal cost, in dollars…

A: In this question we have to find the cost of installing an extra 9 feet of countertop.

Q: Which of the following is a topology on R? {UCR: U is infinite}U{U<R: U is countable} O {[a, b): a,…

A: We will use the definition of Topology.

Q: Problem 2 Show that the compound propositions -p → (q → r) and q→ (p v r) are logically equivalent…

A:

Q: If f is the Fourier series of g(x) J 3, x < then %3D | 16 – a², 0<x < 4 NT f(æ) = + x) + sin 4 What…

A:

Q: Let X be vector space of all ordered pairs. Show that ||x || = |x1| + |x2] defined norm on X %3D

A: It is required to show that: x=x1+x2 defined norm on X, where X be vector space of all ordered…

Q: By Cauchy's integral formula show that, Se" esin e -2n cos(cose) de = 2n; "esine sin(cose) de = 0 0,

A: Cauchy's integral formula : Let U be an open subset of the complex plane C, and suppose the closed…

Q: Show that the map t: V,(R) → V3(R) defined by 1(a, b) = (a + b, a- b, b) is a linear transformation.…

A:

Q: valuate the integral using Partial Fraction Technique: 7- 5) (x – 9)2 dx

A: To evaluate: ∫xx-5x-92dx. Simplifying the expressio using partial fraction decomposition.…

Q: What point on the parabola y = 3 -x is closest to the point (3,3)? Let D be the distance between the…

A:

Q: Match the technique with its appropriate method. Action Sequence is related to While Tape recording…

A:

Q: Show that factorial polynomial represent the function: -1+2r – 3r2 + 42 is -1+ (2 – 3h + 4h²)æ(-1) +…

A: Given function, -1+2x-3x2+4x3 To show that the factorial polynomial representation of above function…

Q: For the function f(x) = 9x² + 12x + 22, find f'(x) f(x +h) – f(x) lim h 0 h O 24x + 22 O 9x O 9x +…

A: Please refer the image.

Q: 6. Analyze the following integral for convergence. I- 2 dr Use two different methods to have two…

A:

Q: Example 2. Simplify X+XABCD+ XB+XBCD+X

A:

Q: 10. Use a triple integral to find the volume of the solid region in the first octant between: z = x?…

A: The given problem is to find the volume of the solid region in the first octant between the two…

Q: Problem #2: The heat index I is the perceived air temperature when the actual temperature is T and…

A: Given- The heat index I is the perceived air temperature when the actual temperature is T and the…

Q: (SR 7.19) According to a Gallup poll, 63% of concession stand workers like the smell of their…

A: Here use normal approximation because sample size is too large

Q: =). Solve the equation zxx = x² + xy² when x = 0, z, = y³ and when x 2, z = y. %3D

A:

Q: What is the main advantage of Newton's interpolation over Lagrange's interpolation?

A: Lagrange interpolation is mostly just useful for theory. Actually computing with it requires huge…

Q: Q2: Based on series solution of Legendre Equation (1-x)y"- 2xy'+ ((l+1)y=0 Find Legendre Polynomial…

A: We solve this using power series of differential equation

Q: 2. A homogeneous thermally conducting solid is bounded by the concentric spheres r= a, r= b, 0b…

A: Let the temperature of inner surface is f1Q=T1. Let the temperature of outer surface is f2Q=T2. Let…

Q: Find the value of lim f(x), if f(x) = 7x + 3 x 7 O 10 O 88 O 17 O 62

A:

Q: The temperature distribution of a homogeneous thin rod, whose surface is insulated, is described by…

A: It is given that

Q: To find a particular solution for y" - 6y' + 9y = x² + 10 with the method of variation of…

A: The given differential equation is a second order non-homogeneous differential equation with the…

Q: Q2. Find the derivative of the function using implicit differentiation tan(x?y*) = 3x + y? %3D

A: