Use the geometric series f(x) = convergence of the new series. f(x) 8 1-x 1 Σx, for x<1, to find the power series representation for the following function (centered at 0). Give the interval of 1-x k=0

Q: Find the area of the surface obtained by rotating the curve y = about y-axis for 1 ≤ y ≤ 3. Area:

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Q: Use the shell method to find the volume generated by revolving the shaded region about the y-axis.…

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Q: -2 2 7e" + dy -5

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Q: Find an equation of the line that passes through the points. (-4, 7), (1, 2) Sketch the line. 10 -10…

A: Equating the two given points,

Q: Consider the level surface given by 2a? + 5y + 2? 4. Match the slices with their correct plots…

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Q: L fx, y, z) ds. Evaluate f(x, y) = 9y – x S: r(u, v) = cos(u)i + sin(u)j + vk Osus", 0 svs1

A: We have to evaluate the integral.

Q: The altitude of a triangle is increasing at a rate of 1 centimeters/minute while the area of the…

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Q: 2. Use membership tables to prove that A - (BnC) = (A – B) U (A – C).

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Q: A product is introduced to the market. The weekly profit (in dollars) of that product decays…

A: topic -rate of change of a function

Q: A triangle has variable sides x,y.z subject to the constraint such that the perimeter is fixed to 24…

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Q: The two-dimensional Laplace equation, f(x,y)= -9x-6y +4 2²f ax 2²f Find for the given function. 2²4…

A: The given function,  f(x,y)=-9x-6y+4

Q: Approximate sin 49º by Taylor series

A: We know that,  49°  = 45° + 4°  = (π/4 + π/45) rad = (45+4)*π/180 =  49π/180 rad

Q: Question 4 If $10,000 is invested in a savings account offering 5% per year, compounded…

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Q: A Norman window consists of a rectangle surmounted by a semicircle. If the perimeter of the Norman…

A: We have to find radius of semicircle and height of rectangle.

Q: 1. Find dy for each of the following: dx 2-x2 a) y= In² 1+x y = Vx+e* c) y = 52r+3

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Q: Find the exact value. (a) sin( (b) arctan (-) (c) arccos (cos())

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Q: the answer is incorrect is not 64pi

A: see below the answer

Q: Consider the second-order differential equation + 25y = 4.5 sin(8t). d²y dt² Find the Particular…

A: The given problem is solved below in detail.

Q: 2. Find the equation of the normal line to the graph of y = x²(1+ In.x) at x = e. Write your answer…

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Q: Find the one-sided limit (if it exists). (If an answer does not exist, enter DNE.) 4. lim (x2 X--3…

A: Given problem:-

Q: Match each function with its derivative. y dy dx ха X a. cos x b. In a • a* ✓ax C. sin x - ✓sin x d.…

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Q: -3x+5 if x ≤ 0 Let f(x) = 4x²-3x+1 if x > 0 Determine each of the following and match your answers…

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Q: Let f(x) = 4x + 8 - 17e. Then the equation of the tangent line to the graph of f(x) at the point (0,…

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Q: Please

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Q: Use calculus to sketch the graph of the given function. (a) f(x) = 3x* – 4x³

A: Given function: fx=3x4-4x3

Q: 2x+1 if x < 2 x²-1 if x ≥ 2 Let_ƒ(x) = Determine the value of ƒ (2). 3 5

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Q: 2/3' 2/2, Suppose 3z? + 2y² + z² = 1 and z = g(x, y) > 0. Determine g, ) and gy 2/3' 2/2

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Q: 2X a) 12 S. Cos(スx) dydx

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Q: Find the interval(s) where f(x) = 2x° – 15x? + 36x – 27 is increasing. -

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Q: w= (2,5) v=(4,2) w+v If we add the two vectors, what’s the correct visual representation of that…

A: SUMMATION OF VECTOR  first vector put as it is  after second is put on head of first vector and…

Q: The population of Canada geese in the Niagara region is increasing at 2% every year. In 2003 it was…

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Q: The director of the school play has to assign 6 lead roles. If the roles are being chosen from a…

A: Using permutations and combination

Q: 1. 12a – 92² + 2 dæ

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Q: For the function f(x.y.z) = sin'(5xyz), find fy. fy. and f (Type an exact answer, using radicals as…

A: f(x,y,z) = sin-(5xyz) fx = derivative with respect to x fx = 5yz/1-25x2y2z2 fy = 5xz/1-25x2y2z2 fz =…

Q: Use the power series E(-19^x", \xl < 1 n-0 to find a power series for the function, centered at 0.…

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Q: Suppose f(x, y) = xy² + 4. Compute the following values:

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Q: Life Expectancy of a Female Suppose that in a certain country the life expectancy at birth of a…

A: In order to get g(t) integration need to be done.

Q: Use the Fundamental Theorem of Calculus to find the derivative of y = cost dt %3D [NOTE: Enter a…

A: Topic = Derivative

Q: : Find f(t) ( Inverse Laplace Transform )of the following functions s+1 1. F(s) 2.F(s) (s +2)+n?n2…

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Q: Suppose that you have the utility function: u (x) = Vx u" (x) 43 %3D Find : u' (x) 1 2x 2x Option 2…

A: I have stated the used formulas in the solution

Q: 1014x + y – 3z = -3 0-x-3z = 13 Bx +5y-4z = 20 %3D

A: Given equations 4x+y-3z=-3              (1) -x-3z=13                   (2) 3x+5y-4z=20…

Q: Integrate the function f(x,y)=(2x+3y+9) when y from 2x to 1 and x from 0 to 1 is Select one: O a.…

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Q: Exercise 195 Further problems on Leibniz's theorem 3. Determine the 4th derivative of: y = 2x'e*…

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Q: 3) Evalnete the itevated integral by Converting the to polar corrdinate, a) dy dx

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Q: 6 Consider the series n2 +n a. The general formula for the sum of the first n terms is S Your answer…

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Q: 2x +4y + 4z = 6 2y+3z = 17 -x + y - 4z = -16 %3D

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Q: Evaluate the following integral. 2 dx 16-x² 0 What substitution will be the most helpful for…

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Q: Evaluate: x - 4 lim x-4x2 - 8x + 16 O Limit does not exist O 4 O1

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Q: y''  +  y'+  2y  =  3e^2x

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Q: Use logarithmic differentiation to find dy/dx. y = Xx + 42 x > 0

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