GIVEN THE FOLLOWING POWER SERIES REPRESENTATION BELOW: x4 + 4! Cosx = 1 - + 6! .. 2! (-1)"x2n (2n)! n=0 a) FIND A POWER SERIES REPRESENTATION FOR X? COS (2X) B) THROUGH DIFFERENTIATION, PROVE THAT: +00 (-1)"(п + 1)12n+1 (2n)! n=0 IS EQUAL TO NEGATIVE T W!

Q: To test the series - 4n e for convergence, you can use the Integral Test. (This is also a geometric…

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Q: - Evaluate the following integrals. 1 1. J x(9 – In² x}5/2 dx

A: To evaluate: ∫1x9-ln2x52dx Let, I = ∫1x9-ln2x52dx

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A: We have to determine the sum of the given convergent series.

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Q: Find the sum of the convergent series tan - ( m til tan M=1

A: This is a telescoping series.  Whose sum is  2/π

Q: m m 2m + 1. m=1 т m 2m + 1 m=1 Do the following converge or diverge?

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Q: find dy/dx. y= (cosx-pix)^(4x)^5

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Q: Given: a, = In(n + 1) – In(n) for n E N || Determine if the following is convergent or divergent.…

A: Given  an = lnn+1 - lnn for n∈ℕ.

Q: A true statement for the function f(x)=2x³-3x²+10 is.... Pernyataan yang benar dibawah ini untuk…

A: The given function is: f(x)=2x3-3x2+10 Now, f'(x)=2(3x2)-3(2x)=6x2-6x=6x(x-1)

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Q: A doll-manufacturing company wishes to create a display box with a square base and open front side.…

A: We have to calculate largest possible volume.

Q: dy Find da and simplify: y = tan(ev)

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Q: dy Find dz and simplify: y=ln[tanh(ax)] where a = constant

A: Topic = Derivative

Q: If substitution technique is used to solve the integral |(12x+3x*)(10x² +x° – 2)´ dx then the -…

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Q: 2m – 2 2m ΣΗ т+ 1 т + 21 m=2 Is it divergent or convergent? 8.

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Q: lim (sin r)tan z T/2

A: Given problem :- Identify the indeterminate form and evaluate limx→π-2sinxtanx

Q: I. Evaluate the following integrals. Зx3—2х2-4х-3 dx x² (x²+x+1) 2.

A: Given: I=∫3x3-2x2-4x-3x2x2+x+1dx   As we know that; The Power rule: ∫xndx=xn+1n+1+C ; n≠-1 And…

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Q: a) Express f(x) = x2ex as a power series. b) Determine the 3rd degree Maclaurin polynomial of f. c)…

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Q: The tangent line equation of x++y“=32 at point (2,-2) is... Persamaan garis singgung kurva x++y*=32…

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Q: 3. 6x° cos (x*) dx

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Q: 62" cos (2") . 6x° cos

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Q: ystem. help (numbers) 2. (See page 530 of the text.) help (formulas)

A: a) Frequency :  T1= 2π/ω =( 2×22/7) / 14 = 22/49 T2 =2π/ω = ( 2×22/7) / 20  = 22/70 T1/T2 = rational…

Q: A rectangular poster is to contain 338 square centimeters of print. The margins at the top and…

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Q: 3) The region bounded by y = x³ – 1 and x- axis on the interval [-1,2].

A: We need to find region bounded in given interval.

Q: and simplify: y = csch² (x² + 1) da Find dy

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Q: Q3) Evaluate triple integral S S dz dx dy . x-y

A: ∫02∫0y∫x-yx+y dzdxdy ∫02∫0y [z]x-yx+y dxdy ∫02∫0y(x+y - x +y)dxdy ∫02∫0y 2ydxdy ∫02 (2y)[x]0y dy ∫02…

Q: Graph the sinusoidal function using key points. 41) y = 1 + cos x 2- 1 -2n TC -1- -27 42) y = 4 sin…

A: Let's find.

Q: Q. 1) The table below gives the readings from a laboratory experiment. Time (t) |3 5 6 Reading (y) |…

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Q: Consider a triangle ABC like the one below. Suppose that B= 113°, a=57, and c=8. (The figure is not…

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Q: In(tan-1x) -dx 1+x?

A: Given,           ∫1+∞lntan-1x1+x2dx

Q: 9. x=t2 +1, y = 3t² + 2t . d'y b) Find dx? .2 Show AllI Work and Give Answer In

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Q: IV. Determine if the given is convergent or divergent. #3. S sin(2 tan¬1 n – n) Σ (2 tan-1n – 1) n=1

A: Solution is given below:

Q: at is the area enclosed by the curve r = 2 cos 36? wer is in square units. Use two (2) decimal…

A: To find the aera.

Q: Find the derivative of f (x) = 4x-10x2+ 8x-2

A: To solve the following problem

Q: Solve [15x/1- xdx . S 3xV3x2 + 4 dx = --

A: 1) the given integral is 15x sqrt(1-x). 2) the given integral is 3x sqrt(3x2+4).

Q: 3-22 – 47 – 3 dr 2(r² +s + 1)

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Q: Given the integral of S cos² x dx,

A: O integrate the given function.

Q: 36) y = 2 sin x - 4 10+y 8-

A: to find the differentiation of given function.

Q: A thermometer is removed from hot water at 100° C into a room at 20° C. The temperature difference D…

A: Answer should be 20.254°C.

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: Determine if the given improper integral converges or diverges. If it converges, find its value.…

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Q: V3/2 1 dx%3D 6). V1- x 1/2

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Q: (e* – e-t)°dt

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Q: Find Duf at P. 1 1 f (x, y) = 5(4+ xy)3/2; P(3,4); i+ j и %3 V2 NOTE: Enter the exact answer. Duf =

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Q: Consider the power series ), Vn² 22n (2.x – 1)" - n² +1 the rodiug ondintorzel of orio

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Q: 6. Find the surface area generated by revolving the curve x = 5 cos' t, y = 5 sin' t, 0sts, about…

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Q: | 62* cos (2*)

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Q: I 3n O The region bounded by y = sin x and x- axis on the interval [-

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Q: What is the area enclosed by the curve r = 2 cos 30? Answer is in square units. Use two (2) decimal…

A: First draw the diagram then find the interval and last intergate it.