5.4-1+1/2 - 1/6 + 1 64 |

Q: Find the radius of convergence, R, of the series. R = Σ 5(-1)"nx" n = 1 Find the interval, I, of…

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Q: Solve Cauchy problem for the non-homogeneous equation: 4 y" +4y' + 3y = 3x, y(0) = − ½, y'(0) = ²

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Q: 6. Σ. 1 n=1 1 ηγη2 +1 n

A: since you have posted multiple question in this question which are not interlinked so i have solved…

Q: 11. Find the absolute maximum and minimum values of each function on the given interval: (a) y =…

A: The given functions

Q: A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the…

A: Let the diameter of semicircle be x feetThen radius of semicircle be  feet

Q: (t²-2t)³ 5t 4. The voltage applied to a 0.25-F capacitor is given by v=- 3.7 s. . Find the current…

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Q: Find the absolute minimum and absolute maximum of f(x, y) = 192x³ + y²(1 - 4x) on the triangle with…

A: Given function is Now, we have to find the absolute minimum and absolute maximum for the above…

Q: Perform the following operations and simplify the results. State the domain restriction in each…

A: The domain is the set of all possible input values  for a which function is defined.

Q: x = 2. (a) lim Below is the graphs of f(x) and g(x), and their tangent lines at YA y = 1.8(x-2) 0 x…

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Q: Find the integral of the following function by parts So 0 sec²0 de Ja where a = 6.08, b = 7.05 in…

A: The given integral is

Q: These triangles are similar. solve for the indicated sides: X X +4 3 LO 5

A: Explaination of the answer is as follows

Q: * Fmd the general solution of :- dy dx = (x²+ 3) + x² 3 2

A: To find the general solution of the following differential equation.

Q: 1. Use the Limit Comparison Test to determine whether the series below converges or diverges. List…

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Q: Use implicit differentiation to find the equation of the tangent line to the function defined…

A: The given equation is; 6x2+2x4y5=8Point (-1,1)

Q: 8. Find the linearization L(x) of f(x)=√√x² +9 at x = -4.

A: Given that the function

Q: Find the limit of the sequence an = (cos.n) 5"

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Q: Use special limit rules to discuss your response, you may use any graphing tool to support your…

A: In a n-sided regular polygon, the angle made at the center is the division of the total angle of a…

Q: Reverse the order of integration and then evaluate [ [ 5y dy dx.

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Q: Find a power series representation for the function. (Give your power series representation centered…

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Q: 4. The financial department of a hospital arrived at the cost function: C(x)=20x³-360x² +2300x-1000,…

A: Given cost function is

Q: Find the exact value of each of the following under the given conditions. 6√85 85 5 sin a = 13 (a)…

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Q: Give two sets of polar coordinates for each of the points A-F in the figure. D E A 0 B F 3 G= T 4…

A: A graph of the polar coordinates of each points A-F are given.The aim is to find the polar…

Q: Find the point on the curvey=+x where the tangent is parallel to the line y = x.

A: The slopes of parallel lines are equal.

Q: 6. Find the sum of the series: 100 x5n−1 n!

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Q: 16. You are designing a rectangular steel vat with a square base, an open top, and a volume of 32…

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Q: Set up and evaluate the triple integral needed to compute the volume of the solid bounded above by…

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Q: Evaluate the integral fx² cos(4- x³) dx sin(4 — x³)+C O -sin

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Q: 3√2 2 [*** 9-x -x² - y² e Evaluate the integral 0 using cylindrical coordinates. Enter an exact…

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Q: Take the logarithm of both sides of the equation and expand it using the product rule of logarithms…

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Q: The first three terms of an arithmetic progression are 2x, 5 and 6 – x.(i) What is the common…

A: The objective of the question is to find the common difference, the 9th term, and the sum of the…

Q: Compute the directional derivative of the following function at the given point P in the direction…

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Q: [120 0230 0 0 2] O [1 20 240 0 0 2] [1 -20 -250 0 0 -2] [200 012 025]

A: The given matrices are

Q: cos(x) - 1 lim 10 esin(z)-1-x

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Q: derivative In 2 x-1 2 x+1

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Q: tanh x = e²t - 1 e²x + 1

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Q: Find the area of the region bounded by the graph of f(X) = Sin X and the X axis on the interval [-2…

A: Given:

Q: Find the degree 3 Taylor polynomial T3(x) of function at a 4. T3(x) = f(x) = (3x + 69)5/4

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Q: Which of the following series are convergent? I. 1+1/2² + 1/3² + ... 1/n² + ... II. 1 + 1/2 + 1/3 +…

A: The given series are; 1) 1 + 1/22 +1/32 +...+ 1/n2+...2) 1 + 1/2 + 1/3 +...+ 1/n+...3) 1 - 1/3 +…

Q: Solve the initial value problem 8y" - 2y' - y = 0, subject to y(0) = -0.2, y'(0) = -0.325.

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Q: Use series to approximate the definite integral I to within the indicated accuracy. 0.5 I = 600 x…

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Q: 3. Solve (3x + y)dx + (x+2y)dy = 0

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Q: Using rectangles whose height is given by the value of the function at the midpoint of the…

A: The given function in the interval .The aim is to find the area under the curve using the midpoint…

Q: If ſ²₁ f (x) dx = 3 and ²₁ g(x)dx = 8, find §²₁₂[4ƒ(x) — 2g(x)]dx -1 -1

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Q: Solve the initial value problem If the solution is y = co + C₁x + ₂x² + C3x³ + C4x² + C5x5 +C6x6 +…

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Q: Suppose that we're setting up a wireless data network for a small municipality. The local ISP wants…

A: The given cost function is

Q: - t+t² g(x) = √3x +z-t dt 1

A: g(x)=∫13xt+t22−tdtProperty of definite integral∫abf(x)dx=−∫baf(x)dx

Q: 2. Prove that (₁ + ²)" is convergent by using the Monotone Convergence Theorem.

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Q: * Find dy dx = the general Solution of :- - X+3x2 √x² + 2x³² 2

A: We use the variable separable method to solve the given differential equation.

Q: Suppose that we're making and selling some widget and the profit (in dollars) when making a widgets…

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Q: By recognizing each series below as a Taylor series evaluated at a particular value of x, find the…

A: A.1+6+622!+633!+644!+⋯+6nn!+⋯