Q.IB) If w=f(u, v) where u = tan ¹2 &v=ln(x² + y²), the show that: Əw dw aw +y ax dy 2- ду x-

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A: Given           εi=Tan β0X1X2β1-sin Yi3 Find ∂εi∂β1 and ∂εi∂β0.

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Q: {G) = -2x+5 firid f(2)

A: To find: The value of f1. Given: The function is fx=-2x+54. Calculation: Substitute x=1 in…

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A: Given x follows a geometric distribution with probability of success  p . We need to find skewness…

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Q: jw F(w). [a - acos (wr)] - A 1 Tjw jwF(W) = -2A (1-cos (WT)). Tjw jwF(W) = -2A (asin ² (WT)) Tjw How…

A: since we have a trigonometric identity:                                   cos(2θ) =1-2 sin2(θ)⇒ 2…

Q: PIND F'): b. FG)- 4- ax*)

A: Given: f(x) = 4-3x25 To find: f'(x)

Q: xP (2) X?-メ-3

A: 1. By Limit comparison test take ∑n=1∞Vn=∑1x32 .And limn→∞UnVn= finite.

Q: Compute : csc(e) d Csc evx dx CSC - Csc cot evx А. 2/x B. csc cot(evF).eF . — cSC Cot csc · cot 2 D.…

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Q: 20. Let (). ()- u = v = If æu + yv = w. (æ, y E R), then a - y = (A) 2/3 (В) —3/2 (C) 3/2 (D) –1/2…

A: To find the value of x-y from the given vectors.

Q: If X = U+v , y =U-V then Show that + 2 du? = 2) ( %3D nene Than ded uce that wok cu+ v*+ (u+v) g…

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Q: d 1) Find sec dt 2)

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Q: e) ay +sina-l, (,a) Equation of tangent 2.

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Q: ag show that: coth's =ţ he (xal/, X-1

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Q: ~(QヘP)=P v~Q =P V ~Q ylgn ihi

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Q: Ir th line x=4+2t, ーも paralled to the plone 3x +ry +2=7-

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Q: AC) = -t+J At - t) sin rdt %3D OA. -t + OB. .3 -t 12 OC. OD. -t + O E. e -- 6.

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Q: c) y" - xy = 0.

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Q: 3T/4 cot e) csc 2 e de T/4

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Q: dy 3) Using the function y=f(x)=x², state which of the following uses of the notation: dx d and are…

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Q: L L'FCE)]> F(4) = 4 sin #t

A: The solution is given as

Q: #6. Eunlwate taldx uhere cosk fa) cosx-SinZx, x)n .

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Q: Suppose Cov(X,Y) = 546. What is Cov(0.13X, 0.41Y)?

A: The objective of the question is to find the covariance of 0.13X and 0.41Y given that the covariance…

Q: ue the differntial equahion 95. X-

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Q: y? lim (х.у)-(1,0) х2 + у? — 2х + 1

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Q: Suppose Cov(X,Y) = 65. What is Cov(0.46X, 0.39Y)?

A: The objective of this question is to find the covariance of the two variables 0.46X and 0.39Y given…

Q: Find all Second partial derivatives fcx.y)- Sin?Cmx+ny)

A: Given that, f(x, y) = sin2(mx + ny) we have to find second partial derivative with respect to x and…

Q: B/let Flx)=[X]-X,x E(-2,2).which valuesof x o E(X) continuaus?

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Q: xxx, xy(Rxy →→~Ryx) - vx~Rxx

A: To prove ∃x Rxx , ∀x∀yRxy→~Ryx ⊦∀x ~Rxx

Q: Q2. If w = f(u, v) , u = cosx and v = sinx, show that: (30 Marks) d?w = v? fuu + u² fvv – 2uvfuv –…

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Q: Suppose Cov(X,Y) = 65. What is Cov(0.46X, 0.39Y)?

A: The objective of the question is to find the covariance of the two variables 0.46X and 0.39Y given…