Write the sum using sigma notation: 1 1 + 2.3 1-2 A B= MINIAN + 1 3.4 DE 1 230 231 TNT MARCU Σ B, where n=1

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Q: Evaluate the integral by making the appropriate substitution: u = 38 fa² (2³ − 1) ³ dx = [ - 38 fx²…

A: Topic = Integration

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Q: Sat) Evaluate the integral using an appropriate substitution. x√1-x dx = + C

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Q: Find the area of the largest rectangle that can be bounded by the positive coordinate axes and the…

A: To find the area of the largest rectangle that can be bounded by the positivecoordinate axes and the…

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A: The given matrix is; [ 0   -2 :  4   3    5 :   2 ]

Q: Find the circulation of F = 6xi +9zj + 7yk around the closed path consisting of the following three…

A: Given ,    F= 6xi +9zj+7yk C1:r1(t) = (cost)i +(sint)j +tk ,       0≤t≤π/2 Circulation   =  ∮c F.dr1…

Q: Let f(x) = x² g(x³). Suppose g(64) = 7, g(48) = -4, g' (64) = 4, and g' (48) = -3. Find f'(4) =

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Q: The Taylor series for f(x) = x³ at -3 is Σ c₂(x + 3)". n=0 Find the first few coefficients. CO C1 C2…

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Q: Find all the values of x such that the given series would converge. 3n (x¹)(n+1) (n+7) n=1 The…

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Q: Find the sum of the first 14 terms of the geometric sequence shown below. 3, 12, 48, 192, ... The…

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Q: Find the k-component of (curl F) for the following vector field on the plane. F = (xey)i + (2ye*)j

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Q: Consider the indefinite integral + U a) This can be transformed into a basic integral by letting du…

A: The given integral is: I=∫lnz5zdz   ....1   Use the common derivative. ddxlnx=1x

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Q: Consider the differential equation (a) Find 71, 72, roots of the characteristic polynomial of the…

A: According to question,Given Differential equation,y''-3y'+2y = 0

Q: An isosceles triangle has an area 200 in ² and the angle between the two equal sides, is π/3. What…

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Q: ∞xk The power series for the exponential function centered at 0 is ex=for -∞o <x<∞o. Find the power…

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Q: 2. Eliminate the parameter in the following parametric equations: x = cos 2t, y = sin t Hint: Use…

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Q: A man wishes to use 141 feet of fencing to enclose a rectangular garden. Determine the maximum…

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Q: in feet, and h the height in feet of the box.) (1, w, h) = What is the volume of the box? ft 3…

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Q: Find the volume of a solid bounded by z = 4 - y2 and the planes z = 0, x = 0, and x = y using…

A: According to question,Given Functions,z = 4-y2,and the planes z = 0, x = 0, and x = y.

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Q: Find T5(x): Taylor polynomial of degree 5 of the function f(x) = cos(x) at a = 0. T5(x) = = Using…

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Q: (4-6) Determine the area bounded by: 4. y=x³-4x and y = x² + 2x

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Q: Find the height of the right circular cone of largest volume inscribed in a sphere of radius 41.

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Q: (d) A satellite orbiting the Earth passes directly overhead at observation stations in Phoenix and…

A: let distance between phoenix and los angeles = x so x = 340 mi angle from los angeles ( θ1 ) =…

Q: Consider the function y = (ex+b)x. Which of the following is true? The function is increasing in its…

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Q: Use the power series f(x) = In (1-x) = -for-1 sx<1, to find the power series representation for the…

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Q: (d) From the right side of a tree Jill measures the angle of elevation to the top of the tree to be…

A: From the right side of a tree Jill measures the angle of elevation to the top of the tree to be 30°.…

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Q: + a x≤0 3). Let /(x)=2e (sinx+cosx) x>0 (B) O 2022 (4) 2 is continuous in (-0, +00), then a= (C) 1…

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Q: 6) Show that (2xy, y, 2yz + + x², y²) is conservative.

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Q: (a) Identify the graph using co-ordinate geometry. Where are the foci located? What are the…

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Q: Determine all critical points of the function y = ln(x² - 6x-40) Critical points at x = -4, x=3, and…

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Q: $1₁² f(x) dx = -3₁ ["* fo If 1. [² f(x) dx = 2 /*18(x) + 2] dx = f(x) dx = 10, and [8(x) g(x) dx =…

A: If ∫-24fx dx=-3, ∫24fx dx=10, and ∫-24gx dx=8, then to find the following integrals.1 ∫-22fx dx=?2…

Q: If the operation is undefined, enter NA. BD = B = sin (a) 4 [362] -9 0 12 8 ar Hint: To create a…

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Q: The sequence given is defined using a recursion formula. Write the first four terms of the sequence.…

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