Exercise 3. * sin(3z) Let f(z) and C: Iz – T| = 1. Then S. f(z)dz = z (z-n) а. О b. 2ni c. -2ni d. None of the above а. b. C. O d.

Q: Exercise 2. * Let f(z) Fa- and C: Iz – 9| = 1. Then f. f(z)dz = sin(32) a. 0 b. 2ni c. 9 d. None of…

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Q: 3. Let f(x, y) = zsin ry. Find: (a) f(x, y) (b) f(x,y) (c) Syy(x, y) (d) fyz(x, y)

A: Given function is f(x, y) = x sin(xy)

Q: sin(32) Let f(z) = z²(z-m) and C: |z – n| = 1. Then f. f(z)dz = а. О b. 2ni с. -2лі d. None of the…

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Q: Evaluate the expression a+b a+b when a=23a=23 and b=45b=45. Write in simplest form

A: # the expressions are printed twice , taking them once given a=23 and b=45 The value of a+b is as…

Q: 5) Proof that: var (3₂)ARI when p= 0 = ß₂ Exy Σ.χ2

A: To prove thatwhen (i.e., when the autocorrelation coefficient is zero), let's consider the…

Q: 5.) Ms. Cyrus has 64 songs on her phone. Two- fifths of the songs are R&B songs. The rest are jazz.…

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Q: Exercise 2. Prove that dim(null T") = dim(null T) + dim W – dim V and dim(range T") = dim(range T),…

A: We prove dim null T*=dim null T + dim W-dim V and dim range T *=dim range T for every T L(V·W).

Q: Let f (a, b, c) = cos (ab) + sin (b) +c where f 7 2'3 Evaluate да af (1 T 7 2' 3

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Q: Let X; = tB¡ B,ds. | Is (X,)r20 a F - martingale?

A: Consider the given process:        Xt=tBt-∫0tBsds

Q: snip

A: Given, cosjx,coskx, ∋j≠k, k≥1 if inner product of two function f(x), g(x) on the interval [a,b]…

Q: (r,1) = (r sin (f), r– cos (1)), (r.1) = (5,-) s numbers in exact form. Use symbolic notation and…

A: In this question, the concept of the Jacobian of functions is applied. The Jacobian of Gr,t is…

Q: 5. Let U ~ U[5, 10] and let X = I5,7) (U) be the indicator function of [5, 7) and let X,…

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Q: 4. §13.3. Q49. Consider function w=w(x, y, z). (a). Find Ow/dx. (b). Find Ow/ay. (c). Find əw/az. w…

A: Given function-We have to find the partial derivatives.

Q: Let f(x, y, z) = 9xy sin (yz) and F = Vf. Evaluate F · dr, where C is any path from (0, 0, 0) to (5,…

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Q: Exercise 3. * sin(3z) Let f(z) and C: |z – n| = 1. Then S. f(z)dz = z (z-n) а. О b. 2ni с. — 2лі d.…

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Q: sin(32) Let f(z) (z-m) and C: Iz - n| = 1. Then fe f(z)dz = a. 0 b. 2ni c. -2ni d. None of the above…

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Q: Əw 1. If w=x" f() show that x ax +y Əw ду = nw where n = integer.

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Q: as Let ĝ +sinh (z?) - ji = 27 where w=f (x,y,2)- %3D Find 2 nd JW and au

A: In the given question we have to find the partial derivatives of with respect to x ,y and z. here we…

Q: Let w = f(x, y) with f E C² and x =h – kh, y = 4k. Which of the following statements are true?…

A: To find  Which of the given statement is true.

Q: Exercise 4. sin(3z) Let f(z) : and C: |z| = 1. Then ſ. f(z)dz = z?(z-n) а. 0 b. Злі с. —6лі d. None…

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Q: Let f(x) = VT, 9(x) = ,. , andh(x) = x². (h o ((h o go f) – f)) (4) = %3D 5-x Select one: a. 4. 81…

A: let f(x) = x , g (x) = 45-x and h (x) = x2f (4) = 4= 2g (f(4) = g2= 45-2= 43h (g(f(4)) = h 43=…

Q: ? Exercise 14.5.2 дz Az To calculate and for the following functions: Ju дv first calculate: Oz Ax…

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Q: Which of the following expressions are not valid? Why? (a) [ f* 1(x, y) dy dz [T (c) [[1(x, y) dy de…

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Q: Let f(x, y, z) = 4xy sin (yz) and F = Vf. Evaluate feF. dr, where C is any path from (0, 0,0) to (9,…

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Q: Exercise 4. * Let f(z) = sin(3z) and C: |z| = 1. Then fe f(z)dz = a. 0 b. 3ni c. -6ni d. None of the…

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Q: 4. If f(x, y)=: Vx² +y? 1 , find f, and f,.

A: Given data is : fx,y=1x2+y2  To find fx and fy

Q: A. Using Mean Value Theorem prove that sin r– sin y| <|r-y for all I,y € R.

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Q: If f(x, y) = x²ye*xy, find fx and fyx.

A: Given function is

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.