1. Justify if the following series is conditionally convergent, absolutely convergent, or divergent +∞o (2) Σ n=2 1 √n(Inn)² +∞o η3/2 (b) Σ η3 n2 −n−1 n=1 +∞o cos(nn) (0) Σ 100 sin(n) + n n=2 80+

Q: Find the extreme values ​​of the function f under the constraint (x^2)/4 + y^2 = 1 by Lagrange…

A:

Q: a. 36. The problem below shows steps in finding the product of two two- digit numbers using this…

A: We find first blank space and then do normal multiplication. For finding first entry let it is x_1.

Q: (a) Perform Gram-Schmidt orthogonalization for the vectors a₁ = , a2 = (b) Find the QR decomposition…

A: Note: We are entitled to solve only one question at a time. As the specified one is not mentioned,…

Q: Q3A) Find normal line and parallel plane to the function f(x, y, z) = x²y²z²-4 At point (1,-1,2).

A:

Q: prove that 1 Ə div A; = {√g grk Ak} = div A¹, Əx* where A; and Ai are the covariant and…

A:

Q: Find the interval of convergence of the following power series. n3x"32 (n + 1)² n=1

A: Here we firstly find the radius of convergence then we check at boundry point then we get the…

Q: 3.ftcost²dt

A:

Q: Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below. y"…

A:

Q: The height of an object, h, in feet when dropped from a height of 1250 feet is given by the function…

A: The given problem is to find the height of the object after 8.5 seconds being dropped from the given…

Q: Solve the given initial value problem using the method of Laplace transforms. y" + 4y' + 3y =…

A: Sol

Q: 5. Suppose that the inverse demand and inverse supply functions are pp = 10- 2x and ps = 4 + .2√x,…

A:

Q: 6. Solve the following system of differential equations y₁ = -2y₁ - 4y2₂ +e-²tu(t), y₁ (0) = 1 y₂ =…

A:

Q: dy B)Solve the differential equation dx x6 +4y ४

A: Given differential equation is dydx = x6+4yx

Q: Consider the taylor expansion of f(x-2^x) in the neighborhood of Xo, the coefficient of is ах2…

A: We have to solve given problem;

Q: let a=2+7i b=4-2i Choose the correct result of a/b O (6-361)/20 O (-6+361)/20 O (-6-36i)/20 O…

A:

Q: n* +2n²+1 no +3 3. Test the convergence of the series an= Ex=1" O Converge O Diverge

A: Given series is an = ∑n=1∞n4+2n2+1n6+3

Q: 2. Take (E = |xi + 1- xi |) Q2 Using the fixed point iteration method solve the equation 2x³-2x-5=0…

A:

Q: Solve using Inverse Operaators. y"" - y'=4e-x + 3e2x; x = 0, y = 0, y = -1, y = 2

A:

Q: A. 1 B. 4 C. 6 D. 7

A: Given that 9+3629×4

Q: Concept Check 3 Evaluate the following integrals and simplify your answers. 1.5(4cscxcotx+2 sec²x)dx…

A:

Q: Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below. y" +…

A:

Q: Q3A) Find normal line and parallel plane to the function f(x, y, z) = x²y²z² - 4 At point (1,-1,2).

A: The given problem is to find the normal line and parallel plane equation for the given function at…

Q: 4. Let r(t) = (t)i + (t-16t²) ; be the position of a particle in a plane at time t. Find the angle…

A:

Q: (Q3) (a) Prove that if (an) and (bn) are sequences such that (an) converges and (an-bn) converges,…

A:

Q: Use the first four non-zero terms of an appropriate Taylor series to approximate Se-x² dx.

A: Here we can use the formula  ex=1-x+x22-x36+.....

Q: The standard form of a quadratic relation whose equation in vertex form is y = - (x - 2)^2 + 9, may…

A: The solution is given as

Q: on the solution for the derivative n=2 it has (-1)d/dx[sin4x] = (-1)4cos4x = 4cos(4x+2pi/2). I am…

A:

Q: (a) Let f(x, y) be defined on (a, b) × (c,d). (i) Give an example to show that existence of partial…

A:

Q: x=4-s+t Find a vector of length √2 which is perpendicular to the plane π =y=1+ s-t z = 1+s+t

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: B)Evaluate the integrals: i) S ii) f/2/2 x 2² siny dz dy dx. rdrde,

A:

Q: struction site, there are 4 excavators. Each one must be allocated to exactly one job. The time

A: The given data is as follows   Job1  Job 2 Job 3 Job 4 1 4 2 5 7 2 8 3 10 8 3 12 5 4 5 4…

Q: Question # 1: Part: a:For given matrix A, find Col(A), Row(A) and Null(A). Also write the dimension…

A:

Q: y" (x) + 4y"(x) + 9y'(x) + 10y(x) = -24e*; when x = 0, y = 0, y'= -4, y" = 10

A: Properties of Laplace transformation…

Q: sin20 B)Evaluate the integrals: i) f/2 inzerdrde, ii) ¹/2 ¹/² finx ₂² siny dz dy dx . 0

A:

Q: 23. DETAILS an If radius of convergence for power series an(x - 3)" is 2,then the series n=1 n=0 A.…

A:

Q: vector v has initial point P₁ = (-1,2) and terminal point P₂ = (x, 14). Find all numbers x so that v…

A: We have to solve given problems:

Q: Suppose that f: R2R is a function given by S x²+y² f(x, y) 0 for xy = 0. Show that f(x, y) is…

A: We have to show the given function  f(x, y) is continuous  at ( 0,0)

Q: k Let n = II p, be a factorization of n into distinct primes P1, Pk. i=1 1 p(n) = n(1 - ²) (1 - ¹)…

A:

Q: Consider the taylor expansion of f(xo-Ax) in the neighborhood of Xo, the coefficient of Əx is

A:

Q: B)Is w = Zez analytical function or not?

A:

Q: Be f(x, y) = 1+√16-y². a) Determine and sketch the domain of f; b) Determine the image of f;

A: For a function z=fx, y, the set of real values of x, y for which f(x, y) is defined is called the…

Q: -16x(2-x)(8+x) For some function f: R - {2} → R we have that f'(x)= = , All the values 6x-12 of x in…

A: Use the following concepts to obtain the solution. The slope of a horizontal line is zero. The…

Q: Find the value of a and b if. a=2&b=9 >ite} sho= &b=3 ܂ 0 " 3 (s+a) +b &b=3 a=-&b=9

A:

Q: B)Prove (cose + i sine)" = cosne + i sin ne

A:

Q: 3. Test the convergence of the series an O Converge O Diverge O Fail test 100 2n=1 n*+2n²+1 75 +3

A: We will check whether the given series convergence or divergeent .

Q: The product -2(t - 3)(t+4) equals

A:

Q: using secant method to find a root, an initial guess Xo = 2, X1 = -1 and X2 = -2 with f(X1) = 4 and…

A:

Q: In spreadsheet of variables view we can define the font variables data format Which command is…

A: In SPSS, we define variables in variable view tab.

Q: B)Is w = Zez analytical function or not?

A:

Q: Using the Inverse Function Theorem, what is (-1) (8) given that f(x)=√6x-2? Note that (11) = 8. (Do…

A: The given function is  t(x) =6x-2  And we are asking to find (t-1)'(8) , to find this first we will…