Determine whether the alternating series converges; justify your ans answer

Q: (a) Which picture below shows a level set of f(x, y, z) = x² + y²? (Notice that f is a function of 3…

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Q: Find the intercepts of the plane 4x+y+10z=40 . Write your answers as points (a,b,c) where a,b and c…

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Q: Let A be a 3x3 matrix such that 23 Assume that the vector v = -2 3 is a solution of the matrix…

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Q: Use a proof by contradiction to prove that , such that 4n+6m=11

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Q: Using the given data set, determine the interpolated value for x = 33 Use Lagrange Method X y 5 -36…

A: x 5 8 11 14 17 20 24 27 30 33 y -36 -49 -96 44 45 37 -26 -46 62 11 Lagrange's Interpolating…

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Q: Verify Green's theorem for a vector field F(x, y) = y²i+z²j and a triangle bounded by the lines z +…

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Q: 5) Prove: v=vu for vectors u, v in V₁. Show all steps clearly, do not skip steps! Use vector…

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Q: Consider the 6-elements set A = {a, b, c, d, e, f}. How many subsets of the set A have 3…

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Q: 7) Given the line L:7=(2t+4, 5-3t, t) and the point Q(5,1,-2). (a) Suppose a plane P contains L and…

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Q: Please finish Solving using. using Gaussian Substitution to the system 2 1 -5 R3-) B 3 + 5 RI -3 -31…

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Q: A fractal pattern has the sequence {1, 7, 49, 343, …}. The explicit formula is _________.

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Q: Utilize the method of mathematical induction. Verify: 1 1x3 3x5 5x7 y 1 (2y-1)(2y+1) 2 +1 for every…

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Q: (e) Verify Green's theorem for a vector field F(x, y) = y²i+z²j and a triangle bounded by the lines…

A: We are given vector field F(x,y)=y2i+x2j For a triangle bounded by x + y = 1 , -x + y = 1 and y =0

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A: Let A has x units B has y units  10000x + 15000y >= 300000Divide equation by 50002x + 3y >= 60…

Q: (c) Give one example where the Green theorem fails, and explain how.

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Q: 35-40 Find the functions (a) fo g, (b) gof, (c) fof, and (d) go g and their domains. 35. 37. f(x) =…

A: We are given f(x)=1x, g(x)=x+1 to find the compositions of the function (fog(x), gof(x), fof(x),…

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Q: Show that x is not a generator of the cyclic group (Z3[x]/<x3 +2x + 2>)*. Find one such…

A: Consider the given cyclic group, Z3x/x3+2x+2* It can be observe that x3+2x+2 has no zero in Z3. So,…

Q: Suppose (X, d) is a metric space and E a non-empty subset of X. Prove that E is disconnected if and…

A: Use definition of disconnectedness mentioned below.

Q: There is an island where all people either always lie, or always tell the truth. You meet D who says…

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Q: A tank initially contains 100 liters of pure water. A brine solution con- taining 2 kilograms of…

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Q: 2. How many solutions could the following linear system have? ax+by=0 cx + dy=0 ex + fy=0 Give an…

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Q: Prove that a nonempty subset U of a vector space Vover a field F is a subspace of V if, for every u…

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Q: Using the given data set, determine the interpolated value for x = 16 Use Newton's Method

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Q: Find the limit, if it exists, or type N if it does not exist. 5zex² + y² lim (x,y,z)→(1,5,5) x² +…

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Q: 100 001 0 0 0 000 30 0 0 1 00 -2 6 -1 0 0

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Q: per triangular nxn matrix. Prove that if CCT=

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Q: Let C be the positively oriented square with vertices (0,0), (1, 0), (1, 1), (0, 1). Use Green's…

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Q: Consider the differential equation (DE):   (xcotx)(y^(13))^(8) + y''-6y'+y= tan(x^5 - x)   a) Its…

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Q: In Z3[x], show that the distinct polynomials x4 + x and x2 + xdeterminethe same function from Z3 to…

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Q: Tracksaws, Inc. makes tractors and lawn mowers. The firm makes a profit of $30 on each tractor and…

A: Solution: Formulate a linear programming model for this problem. Use the graphical method to solve…

Q: Solution of the differential equation - ytanx = y cos²x = -cos zsin²z +c 2 y² cos²x = sinºz+c y³…

A: Given equation is in the form of Bernoulli's differential equation. To solve it, we will convert it…

Q: Given the following vector X, find a non-zero square matrix A such that AX=0: You can resize a…

A: Given information X = 10-3-9 Find the matrix A such that AX =0 . Here, A is a non zero square…

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Q: Approximating the shaded area with the (a) Trapezoidal rule and a step size of h=1 yields square…

A: (a) Given h = 1 and from figure, lower and upper limits are 1 and 3.  The required formula is ∫abydx…

Q: 4 20 785 123 Get det [AB] and det [(1²¹) TB] T A 4 12 13 B = 358 217 =

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Q: If A is normal and no singular prove that so also is A-1

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Q: 1 -2 1 Given A-54 4 -7 3 4-5 2 2 -1 -2 6-4 [1] Compute each of the followings if it is defined. If…

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Q: Find the sum of the first 7 terms of the sequence. The formula for the sum of the sequence is given…

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Q: dy Using variable separable method find y from dx = 3y 2x+1

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Q: Calculus    Verify Clairauts theorem for f(x,y) = 2xe^y-3ye^-x

A: Clairauts theorem is verified