10 8 -20 -18 -5 6 -9 -11 11 11 4 -5 -10 7 -9 1

Q: If sequences {an} and {b} both diverges to infinity, then the sequence an {a}} bn is convergent.

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

Q: Prove the following statement: for all integers n> 1 1³ +2³+ 2 = [ n(n+1)]² 2 + n³ = [ 3

A: To Prove: The following statement: for all integers n≥1 13+23+...+n3=nn+122

Q: (c) Find the limit of the sequence {In(5n³ − n + 1) − ln(7n³ − n +1)} if it converges. Otherwise,…

A:

Q: 16. A cube has a surface area of 150 m^2. Find the edge O 5m 09m 07m 3m 2m

A: To find the edge of the cube we will use the formula for surface area of the cube. If a cube has…

Q: Find the area of the surface correct to four decimal places by expressing the area in terms of a…

A:

Q: f) Below are two charts, Figures 1f(i) and 1f(ii). Briefly explain your interpretation of each in…

A:

Q: 21 40 JJJ. 7yz cos(10x5) dv, where E = sin (2) X = {(x, y, z) | 0 ≤ x ≤ 1,0 ≤ y ≤ x, x ≤ z ≤ 2x}

A:

Q: You have 8 pairs of socks of different colours in one of your drawers [a pair has both socks of the…

A:

Q: ¹ f* (tî + 37 — sin(1) k) dt. Find Ⓒ 2rî Oni +ĵ- k O î+ 2ĵ- k ½a²î + 3aĵ – 2 k 2

A:

Q: Let f(x, y, z) = 9 (√x² − 4y² + 2²) √x² + 16y² + 2², where g is some nonnegative function of one…

A: Mass(dm)=(density at the point f)X(area dA)

Q: Let Let f: R² R² be the linear transformation defined by be two different bases for R². a. Find the…

A: Given f:ℝ2→ℝ2 be the linear transformation defined by fx→=1-23-3x→   Let B=1, -2, -2, 3, C=-1, -1,…

Q: A manufacturer estimates that she can sell a maximum of 30 thousand cell phones in a city. By…

A:

Q: Q.4 Use the one sided Greens function to solve the I.VP. -1 4t2y" +8ty' + y = 3t 2 Int2, y(1)=0,…

A: Introduction: Green's function is a process to determine particular solution of a higher order…

Q: 1. Let S be the triangular region in R³ with vertices at (2,0,0), (0,6,0), and (0,0,3) with upward…

A: 1 Given that S be the triangular region in R3 with vertices at 2,0,0, 0,6,0 and 0,0,3 with upward…

Q: Given: n(A) = 14, n(B) = 22, n(A n B) = 6 Find n(A U B) O 36 O 42 022 O 20 O None of these

A:

Q: 3. Let S be the subset of Mmn containing all matrices A such that (A)₁1 = 0. Determine whether or…

A:

Q: Inside one leaf of the three-leaved rose r = cos(30).

A: In a polar coordinate system, a point is represented with coordinates (r,θ). The radial coordinate r…

Q: Let y = 1 2 and u= 4 2 Write y as the sum of a vector in Span (u) and a vector orthogonal to u.…

A: Introduction: The projection of a vector onto another vector is the application of dot product. This…

Q: Given the cylindrical coordinates: A(5,30°, 6) and B(7, 60°, -3) E. Determine the vector that…

A:

Q: Find the directional derivative of the function at the given point in the direction of the vector…

A: This is a problem of Vector Calculus.

Q: (c) Find the remainder of 9045142161 on division by 247 using Euler's Theorem. [Hint: 247 = 13 x…

A: Euler's Theorem: It states that if gcd(a,n) = 1, then aϕ(n) ≡ 1 (mod n), where ϕ(n) is the Euler's…

Q: Express the following limit as a definite integral. n lim Σ ||P||0 k=1 1 1+2cK The definite integral…

A:

Q: 10. Let A be an n x n matrix such that for every x E R", ||Ax|| = ||x|| (the norm here is the one…

A:

Q: Show directly from definitions that if f(x) and g(x) are real func- tions, bounded on [0,1], and so…

A: Given: fx and gx are real functions, bounded on [0, 1], and limx→0+fx=2 and limx→0+gx=3 We have to…

Q: The circle below has radius 1, and the longer circular arc joining A and B is twice as long as the…

A: The radius of the circle is 1. The length of arc joining A, B is twice of AB. We need to calculate…

Q: Suppose an undamped forced spring mass system is driven by the equation d²x di² where the Fourier…

A:

Q: 8. We will call the integer n doubly square if n is a perfect square and its number of positive…

A:

Q: Obtain the Z transform of 10 s(s² +s+2)

A: Introduction: When the function is given as function of s, it is important to change the function…

Q: Use the branch and bound method to solve the following IP: max z = x₁ + 2x₂ s.t. x₁ + x₂ = 10 2x₁ +…

A: use the branch and bound method to solve the following IP max z=x1+2x2s.tx1+x2≤102x1+5x2≤30x1 ,…

Q: (b) Evaluate the following expectation: E [√" (s² + 2B%) dB₂]. +2B)dBs

A: Here no value of E[t] is given so answer will be in term of it.

Q: QI) A- Find asymptotes for the following functions: x²+2x² (1) (3) B. IF f(x)=√√4-x, g(x)=x², Find :…

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

Q: At noon, ship A was 8 nautical miles due north of ship B. Ship A was sailing south at 8 knots…

A: 1st we will represent the situation in diagram and then use Pythagoras   theorem to find distance…

Q: What region R in the xy-plane minimizes the value of the following expression? [](2² +1 R + y² - 9)…

A: Given, ∫∫R (x2+y2-9) dA   We have to find the region R in the xy-plane minimize the value of given…

Q: 2. Regarding DFT matrix W₁, prove that W 1 = W for N=4. N

A: Consider the given equation, WN-1=1NWNH for N=4 Where, WN is a DFT matrix. So, as we know that,…

Q: 4. The big rectangle has L=9 cm, W= 5 cm. The small white rectangle has this mathematical…

A:

Q: 1. The temperature of a body is measured as 110° F. It is observed that the amount the temperature…

A: As per the company guidelines we are allowed to solved one question at a time so i am solving first…

Q: Home exercise: The function f(x) = 5x¹ + 20x³ 5x4 + 20x³33x² + 2000x + 6 is unimodal on the interval…

A: Given : fx=5x4+20x3-33x2+2000x +6                     -20 ; 10 To find : Roots of the given function…

Q: (x), we - Let (-) be the evaluation inner product on P₂ at -1, 0, and 1. That is, for any p = p(x)…

A:

Q: Define a set X by • 4 EX If a E X, then -x-12 € X - x² € X Prove that every element of X is…

A: A Well defined collectipn of object is called set. Define a set X X = { 4, -16 } 4 belongs to X -4…

Q: The value of a car is given by: 48000 t +3 V (t) where V is the value in dollars, and t is the…

A:

Q: I f(x,y) = sin 3(x+y) over the square 0≤x≤6.0sy≤ 6. R

A: We have to find the average value of function  f(x,y)= sin(3x+3y) Over the given square .

Q: Find a basis for and the dimension of the solution space of the homogeneous system of linear…

A: Solution:

Q: 7. Simplify the following using the algebra of propositions. Show your solutions. a) A = {[QV (P^Q)]…

A: Solution a: Given A≡¬Q∨(P∧Q∧P∧(P∧Q) We can write it as A≡¬Q∨(P∧Q∧P∧P∧Q Using Idempotent law P∧P=P So…

Q: QUESTION 11: if B = {(1,0), (1, -1)}, B = {(1,1), (1, -1)}, [x] = [2 -2]T What is [x] = [a b]¹?

A:

Q: Consider the following function. H(x, y) = In(8x² + 3y²) (a) Find fxx(2,3). (b) Find fyy(2,3). (c)…

A:

Q: 4. Let S be the subspace of P2 defined by S = span{1-x, 1+x, 5, 1-x², 2x}. Find dim(S), and show how…

A:

Q: Let W be a subspace spanned by the u's, and write y as the sum of a vector in W and a vector…

A: Let W be subspace spanned by u's. Here , u1 = 1101 , u2 = -131-2 , u3 = -1011 Also , y = 644-1 We…

Q: 1 (9₁9₁ +) = 9 4 Lagranges equation 2 q 9 find

A: The Lagrangian of a system is defined as the difference between kinetic and potential energy, that…

Q: Discriminant f(x, y) = 2 4 1 = of a function f(x, y) is defined as D = fxx fyy-fy. If 2x² + 2xy + y²…

A:

Q: Use the Chain Rule to find dz/dt. dz dt || z = √√√ 1 + x² + y², x = 2 In(t), y = cos(t) 1 √1+ (Int)²…

A: