We have to determine whether the following series is absolutely convergent, conditionally convergent or divergent. ∑ (-2)^n^2/(n+2)!

Q: 2. Show that 27 | (5²² – 4).

A:

Q: B. f(t) = t³ >= {₁² 0 0 sit 2

A:

Q: x₁ 3 7 9 10 168 120 72 63 Given the table about the function f(x). Construct the Divided Difference…

A: Divided difference table:

Q: Writing In Exercises 7-14, explain why S is not a basis for R². 7. S = {(1, 2), (1, 0), (0, 1)} 8. S…

A:

Q: 6. SET UP the double integral which gives the volume of the solid in the first octant enclosed by…

A:

Q: √4-x² 1²₂ S +*² S-14-x²-y² x dzdxdy

A: As per the question we are given a triple integral and we will evaluate it by changing it from…

Q: Evaluate the integral ff ds, where f(x, y) = y cos(2x) and C is the triangle with vertices at the…

A:

Q: Solve the area bounded by the parabola y2 = 4x and the line y = 2x - 4 in two ways. Answer: 2 sq.…

A:

Q: Define a binary relation =3 on Z by x =3 y if x - y is divisible by 3. 1. Prove that = 3 is an…

A:

Q: Consider the series n=1 (3x)" n Find the interval of convergence of this power series by first using…

A:

Q: Consider the following differential equation to be solved by the method of undetermined…

A:

Q: Let α₁, ₂ and B₁, B₂ be the roots of ax² + bx + c = 0 and px² + qx + r = 0, respectively. If the…

A:

Q: COS b) MTX -L The functions sin orthogonal set on -L≤x≤L, then show (MIX) cos (nIX) L COS L for m=…

A:

Q: 8. Find the centroid of the region bounded by y x and y = x².

A:

Q: If f(x) is a polynomial of degree less than 3, then prove that f(a) (x-a) |1 f(b) (x-b) f(c) (x-c) 1…

A:

Q: 15. Kitchen's Contracting determines that the marginal cost, in dollars per square foot, of…

A: The given marginal cost: C'(x)=4x13The cost is given by:C(x)=∫C'(x)dx        =∫4x13dx…

Q: Find the transition matrix from B to B'. B = {(−1, 4, −2), (1, 3, 0), (1, −3, 0)}, B' = {(1, 0, 0),…

A:

Q: Determine a series solution to the initial-value problem (1+2x2)y′′+7xy′+2y =0, y(0)=0, y′(0)=1.

A:

Q: Find the equation y = mx + c

A: To find the line y=mx+c by using least square method.

Q: Show that 1 3+2 4+3.5++ n(n+2) = 1.3= 1(1+1)[2(1)+7] 6 Simplify S₁ on the right. 3= 3 Is S₁ a true…

A: Given that the statement is Sn: 1.3 + 2.4 + 3.5 + … + n. (n + 2) = [n(n + 1)(2n + 7)]/6 Now let us…

Q: Consider the matrices A = 1 1 [f] U = g h O V = 1 b b X 0 dB = 0 [f a 1 d g 1 C h 0 and X = y. If…

A:

Q: Find four numbers in G.P. whose sum is 85 and product is 4096.

A: There are two question and student didnt mention any particular question to solve so i am solving…

Q: B. Find the volume of the region bounded by the sphere x² + y² +2²=9 x2 + y2 + z2=9 and the planes…

A:

Q: c) f(t) = sin tet d) f(t) = sin t

A: Leatgt=Fs-a Lgtt=∫s∞Fudu where  Lg(t)=Fs

Q: If a, b, c, d and p are distinct real numbers such tha (a² + b² + c²)p² - 2(ab + bc + cd)p+ (b² + c²…

A:

Q: 5. Consider the following linear programming problem: Minimize: C = 4x₁ + 5x2 subject to: 2x1 + x₂ ≥…

A: Given information Linear programming problem:- Minimize:  C=4x1 +5x2subject to:    2x1+x2 ≥12  x1+x2…

Q: Determine whether each of the following series are absolutely convergent, conditionally convergent,…

A:

Q: A. Show that any sequence of positive real numbers either has a subsequence that converges, or else…

A: We have to show that any sequence of positive real numbers either has a subsequence that converges,…

Q: Find the surface integral of the field F(x,y,z)=yi-xj+5 k across the portion of the sphere x² + y² +…

A:

Q: Write the form of a particular solution to y(³) + y" C₁ out determining the coefficients, given that…

A:

Q: Set up the iterated double integral equivalent to ff f(x,y) dA over the given region R: i)…

A:

Q: Evaluate I = f(sin x +9y) dx + (8x + y) dy for the nonclosed path ABCD in the figure. I = D A с B A…

A:

Q: Suppose that f(x, y) = x³y². The directional derivative of f(x, y) in the direction and at the…

A:

Q: If bc + qr = ca + rp = ab + pq = -1, then prove that ap a P bq b cr C 9 = 0. r

A:

Q: 4 Determine whether the sequence is increasing, decreasing, or not monotonic. Is the sequence…

A: A sequence is said to be decreasing and bounded if an>an+1.

Q: Let S be a linear transformation from R³ to R² with associated matrix A = - 2 0 -1 2 2 1 2 Let T be…

A:

Q: We have found the following particular solution and its derivatives. = Ax² + Bx + C + (DX + E)ex Yp…

A:

Q: 12. Find a) L-¹ [24+25 s²+25 + $²-9 10 b) - L -2)³

A:

Q: How many relations are there on the set S = {2, 4, 6}?

A: We know that, the number of relations of a set containing n element is 2n^2. Given that S = {2,4,6}

Q: Set up a double integral to represent the area of region D, the region outside the circle r=3sin and…

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

Q: A raffle is going to be held in which the winner will get $200. If 1000 tickets are to be sold, what…

A: Given, In a raffle, winner will get $200.    We have to find the fair price for a ticket if 1000…

Q: H be the set of all points (x, y) in ℝ2 such that x2 + xy 3y2 = 3. Show that H is a closed subset of…

A: Answer given below.

Q: 1 State Space Systems Consider the state space system 1.1 Is the system stable? 1.2 (3 Is the system…

A:

Q: Determine whether each of the following series are absolutely convergent, conditionally convergent,…

A:

Q: are in A.P., b, c, d are in G.P. and at a, c, e are in G.P. -10 - e

A:

Q: A window has the shape of á parabola above and a circular arc below. Find the area of the window.…

A:

Q: 0 t3 B. f(t) = (10) = {² 0 sit 2

A:

Q: The demand functions for two products are given below. P₁, P2, 91, and 92 are the prices (in…

A:

Q: Suppose that x = (2,1,0,3),y=(3,-1,5,2), and z=(-1,0,2,1). Which of the following vectors are in…

A: A vector v is said to be in the span of the vectors v1, v2, v3, ……, vn if the vector v can be…

Q: Des there exist a geometric progression containing it exists, how many such progressions are possi e…

A: Part A