Green's First Identity Prove Green's First Identity for twice diffe- rentiable scalar-valued functions u and v defined on a region D: I| uv?v + Vu• Vv) dV = || uVv•n dS, where V?v = v· Vv. You may apply Gauss' Formula in Exercise 48 to F = Vv or apply the Divergence Theorem to F = uVv. %3D

Q: In this exercise we need to prove that A complement is a subset of A union L, where L is the set of…

A:

Q: Find the Fourier series of the function f(x)=cos2x.

A: Given: fx=cos2x To find the Fourier series of the given function.

Q: (i) find the curvature of the function f(x) = 4x^2 at the point (0,0).  (ii) find the equation for…

A:

Q: 13. In Z26, it is true that 3-9 = 1, 5-21 = 1, 7-15 = 1, 11-19 = 1, and 17-23 = 1 mod 26. Use this…

A: Modulo is defined as the remainder getting when one number is divided by another number. Modulo is…

Q: Let a and b be positive real numbers. If a, A₁, A₂, b are in arithmetic progression, a, G₁, G₂, b…

A:

Q: Miley rides her wrecking ball during leisure. On a Wednesday, she swings an initial arc distance of…

A: Initial swing : 25 m With each succeeding swing, she travels along an arc that is three quarter as…

Q: t series representation and the region of c f(z) = z+2 6-52 +2²

A:

Q: Let A be a symmetric 2 X 2 matrix and let k be a scalar. Prove that the graph of the quadratic…

A: Given: A is a symmetric 2×2 matrix. k≠0 and  To prove graph of xTAx=k is ellipse, circle or…

Q: Suppose an ellipsoid is described by the equation + 16 9 4 volume of the ellipsoid on the first…

A:

Q: Find the answer and simplify. If possible, write the answer in its rectangular form. Re((−i)−i)

A:

Q: Find the answer and simplify. If possible, write the answer in its rectangular form. Log(3 − 3√3i)

A:

Q: Find the standard matrix, A, for the following transformation E-H = x+y+z 2x-y+z ] 3 T: R³-R² given…

A: Rank-nullity theorem is used

Q: let a= {0,4,9,1.6} , b={0,3,6,12,20} and f a function. from a to b with f(x)=√x + x. A. Find f(0),…

A:

Q: (d) (e) (f) What happens if f(x) is an odd function? Express the following periodic function by a…

A:

Q: A 10-year annuity makes continuous payments. At time tt, the annuity pays at an annual rate of…

A: f(t) = 30 - 3t Therefore the integral is given by: ∫010(30-3t) e-0.05t dt = -3∫010(t-10) e-t20 dt…

Q: 1. Consider the sequence ∞ 1 3 2' 8 5 48 7 384 ...). Answer the following: ) b. Show that Σa is…

A:

Q: (3) (4) (5) day dt4 - y = 0 d²u du +3 dt² dt d²y dy dx² + dx - +3u = 6e-2t 2y = 4x² (Note that the…

A: We have to find the general solution of the given differential equations.

Q: 2. Let C be the semicircle z = 2e where 0 ≤ 0 ≤ T. Show that < C -dz ≤ z² +1 2π√/2 3

A: Given: z=2eiθ , 0≤θ≤π To show: ∫Czz2+1≤2π23

Q: Question 2. The function () is defined as follows f(t)-3-6t+t²,0<t≤4. Define f(t), an even periodic…

A: The given problem is to find the even periodic extension for the given periodic function and find…

Q: in different toys have to be distributed am the number of ways in which these toys c that exactly…

A:

Q: racters of A5 breifly . Answer should be typeed

A:

Q: 2. Let T: R³ → R³ such that T (e₁) = (1, 0, 1),T(e₂) = (0, 1, 1), T(e3) = (1, 1,0). What is the…

A: Given: T : R3→R3 such that Te1=1,0,1, Te2=0, 1, 1, Te3=1, 1, 0. To find: The standard matrix for T.…

Q: Determine the following three vectors {, , } forms a basis for R^3. Expalain your answer.

A: Answer  Given  &lt;2,1,0&gt; , &lt;4,2,2&gt; and &lt;-2,-1,3&gt;  Let check whether they are…

Q: 1. (a) (b) (c) Let S = {(1, 0, 1), (1, 2, 1)} in C³, and W = span(S) Find an orthonormal basis of W.…

A:

Q: 10. Consider the function: f(r) = ¹-. Find all maxima, minima and points of inflection for this…

A: Given: f(x)=x4-x6To find: Maxima, minima, and inflection points.              The plot of the…

Q: Q3 Let f(x) be in L¹((0, ∞)) so that J(0,) f = 10. Determine if the limit lim n→x (0,00) ƒ(x)…

A: Solution:

Q: Find the future value of an ordinary annuity if payments are made in the amount R and interest is…

A: Givan that, R = 100 6.2% interest compounded semi annually for 12 years.  The future value of the…

Q: The time difference between nanoseconds and milliseconds is what?

A:

Q: Triangle ABC has a perimeter of 2007 units, and the sides have lengths that are all integers with AB…

A: solution:

Q: +88 GOZZYTHAI LI... ? Help

A:

Q: Which row exchanges will produce another Sudoku matrix?

A: To Explain : Which row exchanges will produce another Sudoku matrix?

Q: 2. A group of artists have decided to produce hand-drawn cards for Valentine's Day, and donate the…

A:

Q: 1.4 ACSF L5 SC Geometry and Measure: Pythagorus' Theorum Pythagorean Problems In a right-angled…

A:

Q: H = {[x ут X||X, Y |x, y ez} EZ

A: We use the property 1x.x=x and then to find M2x2

Q: Use the Laplace transform to solve the given initial-value problem. 0, y" + y = f(t), y(0) = 0,…

A:

Q: £(+)...m. 1 -2 Fox 2 t fax..... ↓t for a t for 2P=4 1. £. $.2. 4 ............... ********

A:

Q: Let f(x), g(x) be palynomials in 26 [x]. Find f(x) g(x). Write the polynomials as sequence (a, a,,…

A: Given: fx=4x3+2x2+x+3 gx=3x4+3x3+3x2+x+4 are polynomials in ℤ5x. To find: fxgx for the given…

Q: 9. Let P3(C) be a vector space over C and let D: P3(C)→ P3(C) be the differential operator defined…

A: Since you have posted a multiple question according to guildlines I will solve first (Q9)question…

Q: Let A be the set of letters in the English alphabet with the usual order. Define ⟨A2, ≤⟩ such that…

A:

Q: Which of the following represents the answers of all vertical asymptotes beyond the given graph…

A: We will use concept of vertical asymptotes to find points

Q: find the sum of 1X ¹x (2-6) X (2-60²) + 2X (3 - w) x ( 2² w²) + -+ (-1x (m-w) x (m-1²);

A: A

Q: £.(+).. 2 for TS t co for os t.<I 2 t

A: The given function is: ft=0-π&lt;t&lt;0t20&lt;t&lt;π We have to find the Fourier series for the…

Q: Prove that if A and B are both countably infinite sets then A × B is also a countably infinite set.

A:

Q: (a) Let a and b be positive real numbers. If a, A₁, A2, bare in arithmetic progression a, G₁,G₂, b…

A:

Q: Does this exist? I recently learned that there are fractional derivatives and other types of…

A: Determinant is a real-value assigned to a square matrix. Determinants exist only for square…

Q: -8 -5 -1 6 -4 --- U₁ = -5 -6 -7 -10 1 -18 Compute the distance d from y to the subspace of R4…

A: Given: y=-8-1-5-10, u1=-56-61, u2=0-4-7-18To find: The distance, d from y to the subspace of ℝ4.

Q: If the first three terms of the of the sequenes 1/6, a, b, 1/6 are in egeometre Segres hamonie and…

A: The given problem is to find the values of a and b for which the first 3 terms in the given sequence…

Q: A company has three factories, each manufacturing the same product. Let x, y, and z represent the…

A: According to Lagranges multiplier theorem  to maximize f(x,y.z) subject to the constraint…

Q: Show that both R and R² may be covered by countably many open balls.

A: To show :  Both ℝ and ℝ2 may be covered by countably many open balls.

Q: Give an equation for a cosine function that has a maximum at (7.8), followed immediately by another…

A: