If f(x) = Σ n=0 M8 n=0 n + 1 -x" and g(x) = = n+ 2 ∞ Σ n=0 (-1)"+1", find the power series of(f(x) - g(x)). 2

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A: Let, the given function:fx=3+excos 2x

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A: Use division

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A: Basic conversion ways of polar form to Cartesian form are used along with concept of geometry.

Q: 1. Use a trig substitution to evaluate √9-x² 3√3/2 x² -dx.

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Q: c) [ 1: Estimate the area under the graph of f(x) = x² - 1 from x = 1 to x = 3 using four…

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Q: Convert the polar coordinate (5, 1) X = y = to Cartesian coordinates.

A: Note that, cartesian to polar conversion is given by: x=rcos θ, y=r sin θ

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A: We need to solve integral.

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A: Area bounded by two curve  f(x)  and  g(x)  from a to b Area =∫abf(x)-g(x) dx

Q: Solve the triangle, if possible. 38.80 O 25 O B Select the correct choice below and, if necessary,…

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Q: 8. The area of the triangle whose angles are 61 9'32", 34°14'46", and 84°35 42" is 680.60. The…

A: Area of triangle and sine rule are used.

Q: f(z) The residues of 4z (z − 1)(z + 2)² 4/9,-4/9 O 4/9.4/9 O -4/9, 4/9 O -4/9,-4/9 O 4/7,-4/7 O

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Q: Q4: Show if the series is convergent or divergent cos(n) n√√n n=1

A: Solution is given below:

Q: Question [ a) Show all your work. Evaluate 3 L(x-1 (x − 1)√√x + 1dx

A: As per the rules we can answer only the first question and rest can be reposted.

Q: The equation of the plane that passes by P(2,0, -1) and that is perpendicular to the line x-5 2-y Z…

A: The plane passes by P2,0,-1 and that is perpendicular to the line x-5-2=2-y4=z-23

Q: H.W: replace the following polar equations by equivalent Cartesian equation, then describe or…

A:

Q: Introduction to Calculus in Economics (continued): In the previous Problem Set question, we started…

A: The cost, in dollars, of producing x units of a certain item is given by Cx=0.04x3-5x+500a To find…

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Q: Se³x cos (2x) dx 3x

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Q: A fast-food restaurant has a cost of production C(x) = 14x + 160 and a revenue function R(x) = 6x.…

A: Sol Cx=14x+160,R(x)=6xHence , Profit Function P(x) = R(x)-C(x)

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A: We have to find the intersection of plane and line.

Q: (D) sec(a) die (E) sec(z) tan(z) da

A: You want only the sub part d and e to be solved.

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Q: H.W: replace the following polar equations by equivalent Cartesiana equation, then describe or…

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Q: Question 10 Evaluate the following expressions. sin (tan-¹(√3)) cos (tan-¹(1))

A: By triangle property

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A: This question is based on Compound interest formula.

Q: r(x)=x2+5x+4 Find two points on the graph of the parabola other than the vertex and x-intercepts.

A: Solution of given question is written in below steps.

Q: If then is equal to Select one: -2 2 -5 O 5 none of the others [²5(x) f(x)dx = 7 and f(x)dx = 2 ['se…

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Q: H.W: Solve the differential equation y'-(1+x)(1+y²)=0

A: Let's solve given diffrential equation.

Q: Let T be multiplication by the matrix A, find the rank and nullity of T. 1 1 3 A = 6 7 -4 58 rank…

A: We have to find the rank and nullity.

Q: Q5: Find the area shared by the cardioid r = 1 + cos 0 and the circle r = 3 cos 0. Graph the two…

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Q: Sxe 2x dx

A: Integration by parts: ∫u·v dx = u·∫v dx - ∫ddxu·∫v dx dx   We have to evaluate ∫x e-2x dx.

Q: 2. find the derivative of the function g(x, y, z) = 3e* cos yz ,at the point P.(0,0,0) in the…

A: Given problem:- find the derivative of the function g(x, y, z) = 3ex cos(yz) ,at the point P0(0,0,0)…

Q: True or False: The definite integral is equal to Select one: O True False 1² (x² + 3e*)dx [²x²dx + 3…

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Q: A rectangular tank with square base, an open top, and a volume of 10,976 ft3 is to be constructed of…

A: We have a given rectangular box with volume of 10976 ft^3

Q: f sin²(x) cos²(x) dx

A: cos(2x) = 1-2sin2(x) = 2cos2(x)-1. ∫cos(ax) dx=1asin(ax)+C ∫xn dx = xn+1n+1+C

Q: Find the total area of the shaded region shown to the right given by the curve y = 2( sin x)√1+…

A: We can solve this as follows:

Q: ① use First_principle to solve 강종 If y=45-35

A: According to the company rule we can answer only first question and rest can be reposted.