In(z,) – In(-V3 – 1) = -In(2) – 1

Q: 1 Let f (x,y) =In Then f (1, – 1) =... 3x2+4y3 XX

A:

Q: Find the Taylor polynomial of degree 2 centered at a=1 that approximates f(x)=ln(3x) P2(x)=

A: The general form of Taylor expansion of a function centered at a is, fx=∑n=0∞fnan!x-an The second…

Q: - Find the antiderivative, FCx), and Check your answer of the funetionçiven xZ+3x+5 by f (x)=

A:

Q: A. Differentiate the given funetion. 1. y= T* + 4x° -t

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: a²z Find of z= In(xy) a²y

A: When the partial differentiation is done with respect to a specific variable, then all other…

Q: * Show that S i in || + In atx +C using partial fractions а-х

A:

Q: Calculate -1 1 3 2 3 2 3 2 2 using 1 1 1 3 -2 -4 -1 the Gauss-Jordan elimination.

A:

Q: 2- If L(x, y) = ax + by2 is a Lyapunov function at the origin for the system * = y + x³, y = -x +…

A: According to guidelines we have to solve only one question.

Q: Exercise 11. Compute S 60z²(r³ – 5)°dz (11A) 2(r³ – 5)10 +C (11B) 4(r³ – 5)10 +C (11C) 240(z³ – 5)°…

A: We solve this integration with the help of substitution method.

Q: Solve the linear iterative 3 -1 -2 In In+1 6 10 6. 2 -2 -3 -4 Yn Yo Yn+1 Zn 20 Zn+1 envalues are…

A: Given: To solve the linear iterative system, xn+1yn+1zn+1 = 3-1-2-46102-2-3xnynzn,   x0y0z0 = 111

Q: ) Find quadratic least-squares approximation to f (x) = 2*, using ii) Chebyshev polynomials, and

A:

Q: Show that y=y1+y2where y1=c1cos(x) & y2=c2sin(x) is a solution to y"+y=0 and show that the Wronskian…

A: Given  y1=c1cos xy2=c2sin x To show that y=y1+y2 is a solution to y''+y=0 Take derivatives…

Q: 7. Apply the Gauss-Seidel method to Exercise 3.

A: Consider the system of linear equations, 2x1-x2=2x1-3x2+x3=-2-x1+x2-3x3=-6 The objective is to solve…

Q: find the first four nonzero terms of the Taylorseries generated by ƒ at x = a. ƒ(x) = √(3 + x2) at x…

A: Given:

Q: 1 1 Prove that: L' a exp(a't) erfe( avt), where erfc is complementary a+v error function.

A: Formula Used:- L1t=πsLeat=1s-aLerf(at)=as(s+a)Leatf(t)=F(s-a)                   where…

Q: 1+ By using the definition In(1+x) = / 1 -dt, show that for a certain range of values of r, t…

A: Solution:

Q: (b) Find the Wronskian W[y1,Y2](t) of y1 and y2-

A: W[y1,y2]= -t2et

Q: 1. Let z = In(2x2 + y) with x = Vt and y = t. Use the chain rule to find

A: Note:-  We’ll answer the first question since we answer only one question at a time. Please submit a…

Q: If Σ An diverges then > can diverges O only if c>0 O only if c< 0 O only if c+0 O for any real value…

A: Given, the series ∑an diverges, then we have to find the values of c for which the series ∑can…

Q: Q3: Find the Wronskian for the following solutions. Y, = 1, Y =In

A: Wronskian= 112ln1+x1-xd1dxddx12ln1+x1-x= 112ln1+x1-x01x+11-x=1x+11-x

Q: 3. For Z = x²secy,prove that Zxy is equal toZyx

A:

Q: Compute the least squares quadratic polynomial p2(x) which gives the best fit to e x over the…

A: We need to find two things, A least square quadratic polynomial p2(x) which gives the best fit to…

Q: §3.6, Exercise 3. Let 0 1 0 0 0 1 0 0 0 A = Compute C = I3 +tA+ (tA)².

A: Given,  A matrix A=010001000 To compute, the matrix C=I3+tA+12tA2 Where t is any real number.

Q: B. Differentiate the following using Chain Rule. 3.f (2) = (322- 플 + z)" (3=² – +=

A:

Q: Suppose that m>n in the homogeneous system                        a11x1+a12x2+…+a1nxn=0…

A: Here we have a system of homogenous equation with m equations and n variables  Now here m&gt;n which…

Q: In x 2. Use a local linear approximation of f(x) = 1+x² to estimate In (0.9) 1.81

A: Given - fx=lnx1+x2 To estimate ln0.91.81 using a local linear approximation of fx. Here we will use…

Q: (a) FAEN102 students must attend t hours, where t ∈ [0, H], of lecturesand pass two quizzes to be in…

A: The number of students who attend between the time t1 and t2 is given by: ∫t1t220t2dt For the first…

Q: Find the solution x to the least squares problem, given that A = QR in each of the following:

A:

Q: 6. What is the coefficient of x'y" in the expansion (4x + 5y) s. Show your work here:

A: We find coefficient of x7y8 in the expansion (4x+5y)15

Q: Please find all automorphisms. Thanks.

A:

Q: find z- -4 * transform for x (n) = { 2 1 2 3} x(2) = 22 + z' + 2 + 3z x(2) = 2 + z+ 2-2+ 3z %3D خيار…

A: Let's find.

Q: a²z Find of z = In(xy) a²y

A: To find out the double partial derivative with respect to y

Q: 5. Compute the 1st and 2nd degree Taylor polynomials L(x, y) and Q(x, y) for f(x, y) = x /ỹ at…

A: Given function is fx,y=xy Taylor polynomial at point a,b is…

Q: Find the linearization of y = ev7x at x = 16. (Use symbolic notation and fractions where needed.)

A:

Q: Expand xy² + 2x – 3y in powers of (x + 2) and (y – 1) upto third degree | terms.

A: Given ,  f(x,y) = xy2 + 2x - 3y  By Taylor's theorem  f(x,y) = f(a,b) + {(x-a)fx(a,b) +…

Q: Find the maximum value of |2iz+ 3| on |z| < 1.

A:

Q: 7. The function (x, y)= (2x* + y* )exp + xy' is homogenous in x and y of degree

A: .Given,f(x,y) = (2x4+y4) ey2x +x y3Put y= xSo we get,f(x,x)= (2x4+x4) ex2x +x x3 f(x,x)= (3x4) e0.5…

Q: Calculate the residual of P = (1.2, 2.4) with respect to the line 3x + 4y = 12.

A: Here we have to calculate the residual of P=(1.2,2.4) with respect to the line 3x+4y= 12 .

Q: 2. If the Wronskian of y1 and y2 is e2" (x² + 5) and y1 = e2", find y2. %3D

A:

Q: 8. Use the Chain Rule to find az/as and az/at. z = (y-2x)³, x = s³t², y=s+t²

A:

Q: Show that,in LU decomposition, the number of operations required to find U is 2 1 1 for a n x…

A: Consider the process of Gaussian elimination applied to the n×n matrix, A=a11…a1n⋮⋱⋮an1…ann be n×n…

Q: 7] The Wronskian of the functions 1, x, and e -2x is (а) е' -2x (2x+1) (b) 4e-2x (c) -e(2x +1) (d)…

A:

Q: The following equation was obtained by Ordinary Least Squares (OLS): rdintens = 2.31 + 0. 0045sales…

A: Note: Hi there! Thank you for posting the question. As your question has more than 3 parts, we have…

Q: 1 Let f (x,y)=In . Then f „(1, – 1) =...... 3x²+4y3 XX

A:

Q: Calculate the residue of ez.z-5 at z=0

A:

Q: 5. Define the terms : Skewness and Kurtosis.

A: In statistics there are two types of measures namely measures of central tendency and…

Q: If (2, 1) is a critical point of f and fzz(2,1)ƒyy(2, 1) < [ƒzy(2, 1)]², then ƒ has a saddle point…

A: Here, the given statement is: If (2,1) is a critical point of f and fxx(2,1)fyy(2,1)&lt;fxy(2,1)2…

Q: b. verify your answer with Gauss Elimination Method.

A: Given system of linear equation is x-2y+z=2bx+ay=3-2y+z=-4 in the matrix form we can write it as…

Q: min ||y – Hx|3 + A ||x||3 x = (H'H + AI)-1H'y (18) In reference to (18), why is HTH+ AI with A > 0…

A: Given - minx y - Hx22 + λx22 ⇒ x = HTH + λI-1HTy           18 To find - In reference to (18), why is…

Q: y = In[(2x – 1)(x + 3)] with Respect to x by using the chain rule.

A: