Use mathematical induction to prove n(n+1) 2 1+2+ +n=

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Q: 1. I. TAYLOR SERIES - Find the approximate value of sin (0.1) using Taylor Series of 0(h³).

A: To find : approximate value of sin0.1 using the Taylor series.

Q: Let X, Y and Z be subsets of the universal set U. Prove using ONLY definitions (logical connectives)…

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Q: The set of vectors that form a basis are Linearly Dependent Linearly Independent Inconsistent…

A: DEFINATION OF A BASIS-: A SET OF VECTORS v1,v2,v3,..........vn IN A VECTOR SPACE V IS SAID TO BE…

Q: Let f be a function from A to B, and X, Y C B. Show that ƒ¯¹(XnY) = f¯¹(X) ₪ ƒ−¹(Y).

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Q: Consider two real systems, say Ax = b and Cy = d. If the two systems have the same nonempty solution…

A: To Determine: If the two systems Ax = b and Cy = d have the same nonempty solution set, then, is it…

Q: Find the half range Fourier cosine series expansion of the periodic function, f(x)=x-x, 0≤x≤n.

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Q: Find the k-component of (curl F) for the following vector field on the plane. F = (9xe )i + (ye*)j…

A: The given problem is to find the k-component of the curl of the given vector field F=(9xey)i +…

Q: III. SIMULTANEOUS LINEAR EQUATION - Solve the value of X₁, X2, and X3 of the simultaneous linear…

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Q: whose the family of curre intersecting at angle of find the isogonal trajectory of y = = Inx+C…

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Q: Find the sum of the series. ∞ (−1)n 2nx2n n!   n = 0

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Q: IV. Numerical Integration - Find the area bounded by the curve f(x) = (sin x)/x from - 2 to 2

A: The given function is fx=sinxx in the interval [-2, 2]. Our aim is to find the area bounded by the…

Q: Let W₁ = 1, W₂ = √3, W3 = 2 O 0 O 1 0 . ارے and let W= spon! W₁, W₂, W₂}, a) Determine if the set…

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Q: supplier for the automobile industry manufactures car and truck frames at two different plants. How…

A: Given that a supplier for the automobile industry manufactures car and truck frames at two different…

Q: Hello, can you please help me solve this problem? Write clearly and neatly on a paper. Upload it…

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Q: A U.S. $1 bill was valued at 1.256 Canadian dollars in February 2018. What was the value of 27.32…

A: A U.S. $1 bill was valued at 1.256 Canadian dollars in February 2018. We have to find  the value of…

Q: 8. A company wants to assign 8 salespeople to 4 regions of a state (see table below). Region…

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Q: A sequence is given by the recursive definition an = an−1 + 3, a0 = 2. a) Find a1, a2, a3. b) Find a…

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Q: Given V = {(x, y) |x >0} where (x1, y₁) (x2, y2) = (x1x2, y₁ + y2) and c○ (x, y) = (xº, cy), why is…

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Q: The number of vectors that form a basis for P3 is Type your answer here

A: Since you have posted a multiple question according to guildlines I will solve first(Q4)   question…

Q: Let F(t) = (-3t² - 1, t³ – 5tª, – 3t²). Find the line (L) tangent to r(t) at the point (-4,-4, − 3)…

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Q: 1. I. TAYLOR SERIES - Find the approximate value of sin (0.1) using Taylor Series of O(h³).

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Q: 16. Use your calculator to make two lists and a scatterplot for the data below. Find both the linear…

A: The given table of values, x y 0 $22600 1 $18500 2 $16000 3 $15100 4 $14200 5 $13300…

Q: (a) From first principles, find To(x), the Taylor series expansion of (1-x)-¹ about x = 0. Include…

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Q: 02/05 The set of basis vectors {V₁, V2, V3} are augmented to form Matrix A. Which of the following…

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Q: X1 2 1 NII 2 X2 X3 1 0 0 1 0 0 $1 1 82 2 -1 0 1 0 300 500 -1/201 2 3 1 2300 a) What is the maximum…

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Q: (1) Compute f₁ x² dx using a Riemann sum ₁ f(t₁)(x₁ - x₁-1) with a partition that divides [-1,3]…

A: The given integral is, ∫-13x2dx. To Evaluate: the above integral using Riemann sum ∑i=1nftixi-xi-1…

Q: (3.) Let S be the set of all natural numbers of the form prime. S = { P2 Is 1-2, where p and a { P2=…

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Q: Do you identify this equation? What would you need to resolve it? ²u du Əx² at k =

A: This is the heat equation.

Q: Suppose A = - = - { B₁¹=1-4 10 2ģco 62 a) Compute (AB)-¹. -2°207 81 b) Compute det B. BA₂ AJ 1 C)…

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Q: Solve the following system using a convolution integral 9y" + 6y + y = h(t); y(0) = y'(0) = 0.

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Q: Let a plane ax + by + cz + 1 = 0, where a, b and c are parameters, make an angle 60° with the line…

A: The plane ax+by+cz+1=0 The plane makes an angle of 60° with the equation of the line x=y=z and 45°…

Q: Let f: AB and 9: B→C be defined as follows: f(a) = 4a² +2 and g(b) = 26-7 Compute the following: (a)…

A: Let A=B=C=x|x is a real number Let f:A→B and g:B→C be defined as  fa=4a2+2andgb=2b-7 Hence…

Q: Let S4be the set of all strings of 0’s and 1’s of length 4. Define F: S4 → Z nonneg such that F(s)…

A: Using the definition of the function given we answer this question. We just have to count the number…

Q: a) Show how to find an expression for C₁ = f(n) (x) if f(x) = ln z. b) Use this expression to write…

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Q: S Let f(x) be a continuous function on [0, 3] with f(0) = 1. In the Riemann integral 0 Hence x = y²…

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Q: 1. Consider the region bounded by y = e-* + 1, y = 2 and x = 3. a. Sketch the region. Do not forget…

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Q: 32. Determine the finance charge for a credit card during a month which has an average daily balance…

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Q: Le+ A=22 1 Find on orthogonal matrix Q and a 2-1 diagonal matrix D such that A=QDQT.

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Q: f(x)= 300x 1+ et

A: The given function is f(x)=300x1+ex. The given interval is 2, 4 and the number of segment is 8. The…

Q: Jo z(2x + 2y)¹/2² ln(2x + 2y)ds C

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Q: Dan leased a Ford Truck for three years by paying $4000 up front and payments of $185 per month. The…

A: Dan leased a Ford Truck for three years by paying $4000 up front and payments of $185 per month. The…

Q: Prove that 17Z ∪ 7Z is countabl

A: A set X is said to be countable if there exists a bijection between f: X -> N, where N is the set…

Q: Use Green's Theorem to find the counterclockwise circulation and outward flux for the field F = (5x…

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Q: ( › Given 7 = 178/33 -292553/44682 321593/44682 25405/14894 4 -5 53 ال لیا , 5 2 3 -B-0 and -6 7 -36…

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Q: dx dt ) Solve the system with x(0) -6 2 -20 6 2 -1:1 X

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Q: A) x" + 4x' + 13x = te¯t, x(0) = 0, x'(0) = 2

A: We have to solve the given problem by Laplace transform.

Q: Find the indicated vector. tu= [4] ₁v = [7]· F Let -34 °[-2] ° [⁹] 1 . Find 9u - 2v.

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Q: : F[x₁,...,xn] → R such that (1) € = (2) √(x₁) = bi

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Q: A bar 10 cm long with insulated sides, has its ends A and B kept at 0 °C and 0°C respectively. The…

A: The given problem is to find the temperature at any point of time from given data by using heat…