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

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

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: D if x,Y,2 inclepndent Variables and z function in X, Y which achieves the eguation find az…

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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: Determine fx when S(r , y) (x² + 2y)(y² – x) .

A: Given f(x,y)=x2+2yy2-x. The main objective is to determine fx.

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

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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 g(x, y) = 3.2³-6-2²-5.y2 +1. a. ag Show/hide

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Q: af (8,9). Let f(x,y)=x?y*. Find ду

A: We are given: f(x,y)=x2y4 ⇒∂f∂y=x24y3=4x2y3

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: A₁ Let 2 + sinh (2²) - ₁₁ = 27 where w = f (x, y, z)- 1 पुर Find aw дх Jw and Iw > zw. ay dz 3/20

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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: Exercise 3. sin(3z) Let f(z) and C: |z – n| = 1. Then S. f(z)dz = z²(z-n) а. О b. 2ni с. — 2пі d.…

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Q: * Exercise 3. sin(3z) Let f(z) = and C: |z – a| = 1. Then f. f(z)dz = z2(z-n) а. 0 b. 2пi с. —2пі d.…

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Q: 8.Prove the following relationships: a) I(X,Y)=H(X)-HOX/Y)

A: Solution

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

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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.