Find a power series representation for the function: a) f(æ) = x* arctan(2a²) x2 b) g(x) (1+x³)²

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A: A function f is continuous at a point x=a iflimx→a-f(x)=limx→a+f(x)=f(a)Consider at x=-4From…

Q: 3. Use any test to determine whether the series is absolutely convergent, conditionally convergent,…

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Q: (तवन 2.

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A: We know that equation of plane passing throgh the point (x1,y1,z1) and perpendicular to the vector…

Q: 3. Determine whether the following series are odd or even functions. i. f(x) = x² ii. f(x) = x³ iii.…

A: We have to determine whether the given functions are even or odd.

Q: Use a graphing calculator to solve the nonlinear system. y = log (x+ 5) y =x? Select the correct…

A: this question has been solved using a graphing calculator desmos.

Q: (a) Find an equation of the tangent plane to the surface at the given point. хуz %3D 10, (1, 2, 5)…

A: Given:  a)   The equation of surface is   F(x, y, z) = xyz – 10 = 0   given point =1,2,5 On…

Q: Let D and H be the following matrices. 9. D = 1 -3 -1 H = -3 Find the indicated quantity. D - H

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Q: 3" Use the Ratio Test to determine whether the series is convergent or divergent. En=1 (2n)!

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Q: Let B and F be the following matrices. 7 -10 -3 6 -5 4 B= - 10 8 4 -1 -1 6 7 -3 F = -2 -10 -9 6 7 10…

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Q: Find the coordinates (x,y) of the given angles. 1. 10n 4. 45* 5. 270 3. - Sm 6. 330°

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Q: Find the gradient of the function at the given point. Function Point f(x, y, z) = x² + y2 + z* (5,…

A: To find gradient of the function at the given point.

Q: [3 -1 [o -1 2] |4 11 2 Given A = and B=|1 2 |6 1 (a) Find the eigenvalue(s) of BA. (b) On the basis…

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Q: 21 j=3

A: Use the formula for the sum of n natural numbers.

Q: 3. Let u =x² – 2xy+2y' with x = s´ · Int and y = 2s ·t° . au au and at Find as

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Q: Does the following series converge or diverge? 9+8 cos n Σ n' n= 1 The series converges. The series…

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Q: 9. 8- 7- 6- 2 9-8 -7-6 -5 -4 -3-2 123456 789 -2- -3- -4- -5 -6 -7 -8 -9- 9786 654 32

A: Topic = Circle

Q: Solve xy = 8y – 7x, y(1) = -4. || (a) Identify the integrating factor, a(x). a(x) = (b) Find the…

A: Rewrite the differential equation in first order and solve it.

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Q: 7. 5*+2dx

A: This is a problem related to integration of the function. Based on the general formula we will solve…

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A: We have to evaluate the integral.

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Q: The minute hand on the backwards clock rotates counter-clockwise 60 times as fast as the hour hand…

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Q: dx If z4 = x+y2, dy 3, and z > 0, find dz -1, dt at (x, y) = (0, 4). dt %3D %3D dt Please give an…

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Q: The Haycock formula for approximating the surface area S, in square meters (m), of a human is given…

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Q: owing graphs IS fit is continuous/differentiable, and (x) if it is not continuous/differentiable.…

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Q: ) S3x'dx 34- 3/2 3) Ssú dy dt

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Q: Find the remaining trigonometric ratios. Зл T < x < 2 1 cos(x) %3D sin(x) tan(x) %3D %3D cot(x)…

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Q: 6. In the large triangle of Figure 16, m is the weight line (it bisects the side to which the line…

A: 6. The vector which bisects the line joining by two vector heads is the mid-point of the two. So,…

Q: Which method/s can be used to find the volume of solid of revolution of the following? (Choose from:…

A: Note: we have to solve only 1 question so here 1,2 are related so I solve 2 question. Also breif…

Q: ·4 2. 3 a) Find lim g(x), lim g(x) and lim g(x) X+1 -2 x→1+ b) Find f(1). c) Is g continuous at x =…

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Q: Find the volume of the solid generated when the area bounded by the given curves and lines is…

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Q: Match the graph of f, below, with that of its derivative. -2 -1 1 2 3 4 1- -2 4 6 -4+ -3- -6+

A: This question is related to Functions and its derivative, we will solve it using given information.…

Q: please answer the following asap Consider the following IVP: y"- y = 4cos t; y(0) = 0, y'(0) = 1…

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Q: Question 2 Given: y = (sin x) , determine y'/y. O a (sin a)" [cot a+ (1+ ln x) (In sin æ)] (E) None…

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Q: In an insect colony, there are 290 insects after 6 days. If there were initially 80 insects, how…

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Q: 2. If f(x)=x² – 5x find, a. f(y? + 1) b. f(z+1)-f(z-1)

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Q: 3. Find the equation of the plane through (-3, 8, -8) that is perpendicular to the plane 7x– y + z =…

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Q: 2. Use the Mean Value Theorem to show that f(x) = 2x sinh(r - 1) +2"- x has a critical number…

A: We prove that f'(c) =0 , here c is critical points.

Q: You have $7000 to invest for seven years. Which investment will provide the greater return:  5%…

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Q: X Your answer is incorrect. Edit Find the vectors that satisfy the stated conditions. NOTE: Enter…

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Q: (2x - 5y + 3)dx - (2x+4y - 6)dy = 0

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Q: Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of…

A: Here, the given function is: f(x)=x2x2+3 That can be rewritten as: f(x)=x2+3-3x2+3=1-3x2+3

Q: Determine if the following statements are true or false. (a) A square matrix has an inverse if the…

A: We have to determine if the given statements are true or false.

Q: Calculate -2 + lỉ. Give your answer in a + bi form. In polar form, use the angle 0 <0 < 2n. a - b -

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Q: Consider the following lines 4:z=1,y-1=-4,2=1-3t :z=28+1,y=1-3s,z=1 y+1 3 z-1 %3D %3D За 2a Find the…

A: We have to find the point - normal equation of plane.

Q: Example Find the exact area of the surface obtained by rotating the curve y? = x + 1, 0 <x< 3, about…

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