Given w =< W1,W2, W3 > Prove or disapprove: w · w = ||w||. Explain all detail-

Q: (c) Suppose that o is differentiable. Prove the identity | øVø •n ds : (OV²ø+ V¢ • V¢) dA

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Q: Let f(æ, y) axy + az?y+ y³. (a) div(grad(f)) = (b) Find a so that div(grad(f)) = 0 for all æ, y. %3|…

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Q: When z = f(x,y), which of the following is true for the whole statement? %3D

A: We have given function z=f(x,y). We need to check which of the conditions are true for the given…

Q: Find the value of c such that S xe = 3.

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Q: That is, T'(1) = %3D

A: Given, a recurrence relation T(n) corresponds to the natural numbers, but that "skips" multiples of…

Q: Let f(2)= ¹5 and let C = {z € C : |z| = 1}, described in the positive sense. Determine the value of…

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Q: If f(x, y) dA > 0, then f(x, y) > 0 for all (x, y) in D. True False

A: Given statement, If ∫∫Df(x,y)dA≥0 then fx,y≥0 for all x,y∈D. The objective is tell whether the…

Q: • Given f(x, y, z) = x² In(x + y- z), find f(2,4, 5). а. 0 b. 1 с. 2 d. 3 O a. b. С. O d.

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Q: Vx e Z, 3y e R, y² = x

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Q: Select the best option based on the information below. MP at(x;,x;). = TRS = MP, %3D %3D - W2 Select…

A: Given....

Q: Use the fact that dim(R(A)) = dim(C(A)) to explain why rank(A) = rank(A").

A: Here we can use the fact that  rankA=dimRA to prove the identity.

Q: Q#2 In the ing a unit Z[x1.Show. that is

A: To Show -    Concept used -

Q: 2. Find the correct value of c such that P (Z < c) = 0.4. %3D C =

A: According to the provided information, P(Z&lt;c) = 0.4

Q: Given EF is tangent to OA at point D, which statement must be true? Select all that apply. E D F A.…

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Q: Evaluate and simplify y'. In x where a is constant y In x + a

A: Given:   y=lnxlnx+a

Q: Evaluate the following. (Give an exact answer.) (x, y, 2) dS x² + y² + :2 f(x,y,z) : %3D x² + y? S:…

A: The value of the given integral is 64/9

Q: evaluated at fo as follows. 1 0.5 0.2

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Q: Q5: For which values of z is w =1/(z – i), defined? For these values obtain and v and evaluate w…

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Q: Given f(x, y, 2) = In(x² + y? + z?), show that 2 dy? x² + y² + z²

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Q: (c) Suppose that ø is differentiable. Prove the identity $Vø•n ds |(V*o+ V¢ • Vø) dA

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Q: Let f(z,y) = z* + y° – 2r° - 4y be given. Which of the following statements is correct? %3D

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Q: Given the multiple variable function f(x, y, z)= Ax*e» - Bz cosx*y°)+Cx*y*z?, where the coefficients…

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Q: Define h(*) = J¿r)d* . Then, which of the following are true?

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Q: Given f(x, y, z) = 5x² + 3y? + 2z², find fr(x, y, z) = fy(x, y, z) = %3D f-(x, y, z) = %3D

A: We have to find partial derivative

Q: DS tan %) c(x) ax

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Q: Find a, b > 0 such that the following equality holds: {r €R : -a < br – 3 < v2} = [-3, 3).

A: Note the result : The set can be represented in interval form as .

Q: Need help on showing how to prove this      (x(y+z))w=(xy)w+x(zw)

A: Expressions are mathematical statements that have a minimum of two terms containing numbers or…

Q: given f (z) = (z + 1)° – 32' what is the value of u (금, )

A: Topic:- complex number

Q: Consider the relationship R C N x N, R(x, y) holds iff (/æ /T) E N. True or False R is irreflexive…

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Q: Let f (x,y) = e**ytan (x + y), find дудх

A: Explanation of the solution is given below...

Q: prove that 16 x (I+x) dx 306

A: The product rule of integration states that∫fxgxdx=fx∫gxdx-∫f'x∫gxdxdx.

Q: g(x)]dx, (b> a), for all f, g € X. Show that (X, d) is a me

A: Matric Space

Q: Find the constant C such that * x3 – 3x + 8 < C, where x e [0, 3] | 18 O 23 14 17 O 26

A: We have to find c

Q: Given that f"(x) = cos(x), f'(a/2) = 13 and f(t/2) = 14, find: %3D %3D f'(x) = f(x) =

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Q: Q5: For which values of z is w =1/(z - i), defined? For these values obtain u and v and evaluate w…

A: Given that: w=1z-i, z=1-2i

Q: What is r' (x) when r(x) = In ? Select the correct answer below: O Pu) = - Sr+1 O rw = - Sr+1 x) = !…

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Q: If f(z) = 6tan(z) , then f'(r) = (A) In(6) 6tan(2) (B) sec2(z) 6tan(2) (C) In(6) sec2() 6tan(z) (D)…

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Q: Given: EF | RS Prove: a. AFXE ~ ASXR FX b. SX EF RS S X- E R

A: Given, EF||RS

Q: Let f(x, y, 2) = eF tan(x² 2) . Compute fay: (x, Y, z) . Simplify your final answer.

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Q: Determine all values z ∈ C satisfying  e^z = −2i.

A: ANSWER :

Q: F Given: ABCX is a O: DXFE is a C. Prove: ZB = LE X, D

A: Given that, ABCX is a parallelogram and DXFE is a parallelogram. We have to prove that, &lt;B =…

Q: Let f(x, y) = y? – x? and g(x, y) = e²+y. Verify that div(ƒVg) = fV²g+ VƒVg.

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Q: Iff, g e R(x) on [a, b), prove that f? dx + g? dx 2 2 Ifg | dx.

A: Given that, f, g∈Rx on [a, b]We need to prove that∫abf2dx+∫abg2dx≥2∫ab|fg|dx

Q: Given f(x,y)=x-exy, evaluate fy(3,0). 06 O 27 O 9 O 13

A: topic- partial differentiation

Q: If f(x, y) 3D х'у? — 2x'y + 3х, find (а) f.(x, у) and f,(х, у), (b) f:(2 , –1) and f;(2 , –1)

A: To find partial derivatives of f(x,y) = x3y2 - 2x2y + 3x To find :- (a)fx(x,y) and fy(x,y)…

Q: For Z= x²csc y,prove that Zxy is equal to Zyx

A: Given that,    z=x2csc y

Q: Use the properties of E(X) to prove that E(aX +b) = a E(X) + b.

A: For a random variable X, the expectation of X is defined as E(X).

Q: ue of a and c are and

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Q: Find the number c that satisfies the conclusion of the Mean Value Theorem on the gi does not exist,…

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Q: Which value for z is a counterexample to the following statement? For all positive values of x, x >…

A: counter example = an example that opposes or contradicts an idea or theory.

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.