owing determinants and justify your answers. 1 2 3 4 1 a q² 2 2 3 4 5 a 1 a a² (b) (c) 3 3 3 4 5 a² 2 a 1 a 4 4 4 4 5 a³ a² a 1 5 5 5 5 5 ST

Q: A. The variables x and y satisfy the following coupled first order differential equations. dx =x-2y…

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Q: upto the fifth approximation of the equation dy/dx = y + x, such that y = 1 when x = 0. Check your…

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Q: Q1: Find and sketch the domain for each function. 1 2. f(x, y) = In(4-x²-y²) 2. f(x,y) = cos ¹(x −…

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Q: Example 8.16. The velocity v of a particle at distance s from a point on its linear path is given by…

A: This problem is solved using Boole's Rule.

Q: D = 3 1-2 0 0-4 ** 5 -4 5 3

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Q: 8. Find two linearly independent power series solutiions centered at x = 0 to the differential…

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Q: Given the f(x)=cos(x5)+ln(x), find f’(9) at h=0.8 using: (Round off the final answer to 3 decimal…

A: Given that fx=cosx5+lnx Find f'9 when step size is 0.8 using (1) Forward difference method.

Q: Which characteristic/s implies(y) that a set S of real numbers is closed? S has no accumulation…

A: If S has no accumulation point that's does not implies that the set S is closed. Counter example is…

Q: (b) Given the set S = [-1,1] and the function g: S→ R defined by g(x) = that g is one-to-one, and…

A: g is one to one because  For every x there is a different image in g(x) if x= -1 then it's image is…

Q: Find a plane that contains S and is perpendicular to the plane that contains the points

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Q: 1 If x is in S, then x may be a boundary point and an interior point of S. N S A 2 If a set S has…

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Q: A competitive firm recieves a price p70 for each unit of its output pays a price wro for each f its…

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Q: et f(x) = n 0, if xe Qor x = 0 if x= min lowest term . Compute for ff. " n

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Q: (a) True or false? If you state true, then prove it, otherwise provide a counterexample. Given A, B,…

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Q: Which characteristic/s implies(y) that a et S of real numbers is closed? S has no accumulation…

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Q: a. A11=4; A12= 4; A13= 2; A21=3; A22= 1; A23=1; A31= 2; A32=-5; A33= -1

A: As per the policy, we are allowed to answer one question at a time. So, I am answering the first…

Q: Which among the sets is open? O [0,1) O (01/1/3,1/2,1} R\[a,b] None of the above.

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Q: Consider a function defined on R² by f(x, y) = y(x + 1)(2 − x − y). (a) Find all four critical…

A: The given problem is to find the critical points of the given function of two variables and also…

Q: Σ[1] (b) Test for convergence or divergence for the series

A: We solve given series by limit comparison test

Q: Evaluate the double integral that will find the volume of a solid bounded by z = 1-2y² - 3r² and the…

A: Given that,A solid is bounded by z=1-2y2-3x2 and the xy-plane.The volume of the solid is determined…

Q: ¹ Find the value of L-1 s²+6 [(s²+1)(s+4)]

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Q: 1. You are to program a robotic arm on an assembly line to move in the xy-plane. Its first…

A: Note :As per our policy, we are allowed to answer only first two parts of question kindly post…

Q: b) Let T:R³ R¹ be a linear transformation, and let B = {e1, ez, e3} be the standard basis for R³.…

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Q: 4. 5. For n E N, { x ER | |x-x*|<1/n } is open. UA_n is open where A_n=(n-1,n).

A: To determine: If the given statements are always true, sometimes true, or never true: (4.) For n∈ℕ,…

Q: 2. Consider the following four functions from R into R, determine if onto or 1-1 function. Support…

A: To find out which of the following function is one-one,  onto .

Q: Six second-order equations and four y(t)-graphs are given below. For each y(t)-graph, determine the…

A: As per guidelines we can do only 3-subparts.

Q: 7. Yoshi is experimenting with an image-editing program on his computer. He rotates his picture…

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Q: Question 3. F Prove each of the following. (a) Given a real number a > 1 with a N, show that there…

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Q: Use the square root property to determine all real solutions for each of the following equations.…

A: part-1 part-2

Q: 4. (a) Show that the outward flux of the postion vector field F(x,y,z) = (x)7+ (y)] + (z) through a…

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Q: Use the function & and the given real number a to find (F-¹) (a) a = 2 *7-3, F(x) = * +7 22+3 (F-1)…

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Q: Which among the following diagrams correspond to the metric below on the real plane R^2?…

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Q: Find the first approximate root of the equation 2x^3-2x-5=0 up to 4 decimal places using Xn=1.5…

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Q: of a matrix is the factorization of a given square matrix into two triangular matrices.

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Q: Find the sum of 73 75 + [ 2ㅈ 11.3 13.5 ㅈㄱ 15.7 + + (-1) 7- 2n+1 12n-1 (2n+1)

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Q: Ex. Locate the centroid X of the shaded area shown. 1m 1m X

A: Calculate the area A of common region between the curves y2=x that is y=x and y=x2.

Q: 4. Evaluate the following determinants and justify your answers. 1 a 1 a a² (b) (c) a² a 1 a a³ a² a…

A: Note: As per our policy, we are allowed to answer only first two parts of question kindly post…

Q: What are all the transformations that could have been form in the picture ?

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Q: (b) Given two metric spaces X,p>, and a function f : X→ Y that is uniformly continuous on SC X. If…

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Q: Let N = (0, 1) and 1 0 such that ||9n||LP (2) ≤ M, VEN

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Q: If R is commutative ring then deg(f(x) + g(x)) = max(deg(f(x)), deg(g(x)). False O True

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Q: Q3/ Find the volume of the solid generated by revolving the region bounded by y = 3/(2√x), y = 0 &…

A: We have to find the volume of the solid generated by revolving the region bounded by y=32x, y=0 and…

Q: 2. Evaluate dx da da -S /////VE-VE b. C. 1+ a.

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Q: Example 8.28. Apply Simpson's rule to evaluate the integral 2.6 4.4 dxdy I = left xy

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Q: UA_n is open where A_n=(n-1,n).

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Q: III 1. dt2 fip +6- dt and the gen +8y=2e-3t am to nor 2. d'y dt2 fip +4 +13y=et dt 3. +10y = e

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: rated, i.e. for each z EL v on the left is K4 and E

A: LetF (n)denotes the number of perfect matchings ink2n. Then, Clearly a₁ = 1. Now, ink2n, (where n…

Q: Determine (without solving the problem) an interval in which the solution of the given initial value…

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Q: Find one particular solution to the following second-order forced equation d²y dy +8 + 15y = 5…

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Q: 8. We know that P₁= P2 on B3 if P₁ = P2 on C, provided that C generates B and is a 7-system. Show…

A: Solution :-