Let X; ~ X"(1) i= 1,2, . - ·, n and assume they all uidependent are Y = Ź Xi %3D しニ」 ان منتتفينتمنل ۷ Y? What is tle P Show Y 1 T'ieuition

Q: の x?. xy- yーx find %3D of 3 f Fex)こ X²+5x+2 Find f cl Q Let texl= goe) Find fezt ifgeziz=3_ find…

A: Differentiating the functions

Q: 4)Given determine

A:

Q: Q2. Consider the ODE Using u = y ¹, we get A) u' - xu = sin x B) u + 2xu = - 2 sin x C) u + xu = sin…

A: The given differential equation is       y’ - xy = y2sin x    . . . . . . . . . . . . (1)    Now, we…

Q: (2) DE (D² D²-70³-11 0²-80-12/9=0

A: A detailed solution is given below.

Q: Əz Əz and at Use the chain rule to find as || 8」8 z = tan (#). u = 7s + 9t, v = 9s - 7t

A: answers are given below.Explanation:

Q: dr For f (r+3)3-(r+3)7

A: This is a problem of substitution.

Q: у У1 Уз Уч У 4 | Уб 6 У 7 У 7 64 If y = cos ax, prove that У 2 5 = 0, where y, Ув 8 = dr ту. dx'…

A:

Q: let Po)- tar'c) + tant (L). show that Plx)=C,where cis a constant and then Aind C

A:

Q: 6. Prove that ſex*dx+rydy = Sc r*dx+xydy+Sc, r*dx+xydy+Sc, x*dx+ rydy.

A: Prove that: Where c is the curve of the integral. The curve c is divided into piecewise region.…

Q: cos cos 21/3

A:

Q: H.w: Salve the ditterential agquahons- O (I+x)y =0 +xy and find the Particular salulion whan yrol=z…

A: We use separation of variables to solve these differential equations.

Q: If u = cot ди then x x- y

A:

Q: d6 1 2-₁ {-101 = ds6(s-7)2-64, 13. If L-1 6₁)} = atbect senh(8t), the value of (a.c) is:

A:

Q: Find dy Ser ysX"+3*+ e° dx + sin (1nx)

A: Given that: y=xy+3x+ecos-1x+sinlnx

Q: Find the length of (3e' – 3, 4e' + 7) for 0 <1< 1.

A: Arc length of a curve between two points is the distance between the two points with the restriction…

Q: 2) al X,X2 =) y = Xi~ ? ,-,Xn ~lid exporen tíal ( 100 b) Xq, X2,--- Xn~ iid N(44i44)= ビ- ~? i=1 %3D…

A: Solution : a) Given : xi  ~ exp ( 44100 )   ; i = 1,2,3,...,n ∴ θ = 0.44     Y    = ∑1n Xi It is…

Q: If ACX,find A' for(X.I)

A:

Q: Prove that x² = 13 (1²) + 1) = (xin(e))) ১0 sin(0)

A: Given  x=rsinθ cosϕy=rsinθsinϕz=rcosθ To prove :∇2=1r2∂∂rr2∂∂r+1r2sinθ∂∂θsinθ∂∂θ+1r2sin2ϕ∂2∂ϕ2

Q: Renirite ecc of the fo1lawing buuting ఆUng (A10garithm oto singu algebraic quantity) - Inca) -'/3…

A:

Q: 660. Let A = (1, 5), B = (3, 1), C = (5, 4), A' = (5,9), B' = (11, –3), and C' = (17, 6). %3D Show…

A: according to the problem, we have

Q: (e") = :一

A: Our aim is to find the derivative of eπ i.e, ddx eπ =?

Q: How would you shade B'n(E' u D) on a vinn diagram

A:

Q: for 3x'z -x'y² +2z + 3xy = 0 ( Hint: Let %3D F(x,y,z) = 3x z - x'y? + 2z +3xy) %3D

A: Explanation of the answer is as follows

Q: For any natural number m, evaluate 1/m +x")( 3m 2m 2m +x 2x +3x" +6)"* dx, x > 0. m X

A: Topic:- Integration

Q: Which of the following integrals will give the volume of the the solid formed by revolving the…

A: Here we will find out the volume.

Q: Find L{t*e* } (s-3) 2 (s-3)2 1 (s-3)2 2 (s-3)3 2 (s-3)

A: We find Laplace transform of t2e3t

Q: 5) f(x.y)= *+y

A: We are solving the first question and for the next question post the question again andalso mention…

Q: x+1 dx x(x+3)(x+2)(x-1)

A:

Q: Exl Let c R,Z) be usual toP s Pace and A-fcxy)ER/ x²+y²< 13 find A Ext CA), Ā , A°

A:

Q: Prove that ²-1 (²) (0) (sin (+,-) + do r² sin(0)

A: Given : ∇2=∂2∂x2+∂2∂y2+∂2∂z2 To Prove : ∇2=1r2∂∂rr2∂∂r+1r2sinθ∂∂θsinθ∂∂θ+1r2 sin2θ∂2∂ϕ2

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.