Evaluate the following integral as power series.

Q: dx Q1. 1+x+x2 ,

A: Given: - The indefinite Integral is, I=∫dx1+x-x2 To find: - The solution of the indefinite integral.

Q: f(cos*x- sin *xkx *a

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Q: f(x) = cot? 1 %3D tan-1

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Q: QUESTION 2: Find a counterexample for the following statement: For all x ∈ N, x^2 + x + 41 is a prim...

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Q: f) = In(tanx) -1 %3D

A: ddxlnarctanx  

Q: 39. For each condition, find unit vectors å and b or explain why no such vectors exist. (a) |a+헤-0 (...

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Q: Use Lagrange multipliers to find the maximum area S of a rectangle inscribed in the ellipse 25 = 1 (...

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Q: Evaluate the following indefinite integral. Use C for any constant of integration. 4x³ + 8x² + 75x +...

A: ∫f'(x)f(x) dx = ln f(x) +C ∫xn dx =xn+1n+1+C ∫1xdx =lnx+C ∫1x2+a2 dx = 1atan-1xa+C

Q: Let D be the region enclosed by y= sin(x),y = cos(r), x 0 and r = = 1. The volume of the solid forme...

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Q: Q.4. locate the critical points of the function f(x)=x*(x-1)³ and identify critical points which are...

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Q: The numbers of words defined on randomly selected pages from a dictionary are shown below. Find the ...

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Q: 9. There is an infinite discontinuity at x = 0 and f(0) = -2 10. There is a jump discontinuity at x ...

A: Let's find. 

Q: 3k +1 a) Let ak = 2k Find ak k=1 (– 1)" b) Let b, n2 + 1 2 Find bn n=0

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Q: Differentiate the following inverse trigonometric functions : 1) y -2 sin-1x 2) s (t) =-cos-1 t

A: We will ise tha fact that  Derivative of sin-1(x) is 1/√(1-x2) and that of cos-1(x)=-1/√(1-x2). And ...

Q: The curre y=J36 - z' , -4£ x s4 will be rotated about the ルーaXis. find the area that results af the ...

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Q: Find y ′ and y″ by implicit differentiation. x2 + xy + y2 = 5 y ′ = y ″ =

A: We have to find  y ′ and y″.  Given x2 + xy + y2 = 5

Q: Given the differential equation 213y" – xy' – 20y = 0 Determine the General Solution for the differe...

A: see below the answer and explanation

Q: Find the arclength of y 2x +1 on 0 < x < 2

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Q: Find the derivative of the given function at a given number. 1. y = 3x² - 2 at f'(1)

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Q: 9. An amount of $12, 000 is deposited in a bank that pays interest at a rate of 3.5%, compounded con...

A: Given :Total Deposited amount = $12,000Rate = 3.5%Time = 4 years

Q: Determine whether the sequence converges or diverges. If it converges, find its limit {2-(4/n)} Th...

A: See the details solution in below

Q: 20 w(x) = x' + 7x3 3 1 v(x) = e² s(1) = r*e* 1² – 2 q(x) =

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Q: (1) In this question we will find a recursive formula for the integral In = [ (In 2)" dr. (a) Find I...

A: We will use integration by parts formula and after get the reoccurrence relationship we will use tha...

Q: Use the ratio test for absolute convergence to determine whether the series converges or diverges. I...

A: Given Series ∑k=1∞-27k

Q: Find the equation of the tangent line to the graph of f(x)= (x/x+3)^3 at x= -2

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Q: Using variable separable technique, find the general solution of (4x+xy^2)dx + (y+x^2y)dy = 0

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Q: Determine whether the series E " *" converge or diverge using alternating n+1 series test. o (-1)" D...

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Q: Evaluate the triple integral. x dV, where E is bounded by the paraboloid x = 8y2 + 8z2 and the plane...

A: Here, the given solid E is bounded by the parabolid x=8y2+8z2 and plane x=8

Q: Evaluate the following definite integral. No decimal entries. Find exact value. 19 15х + 7 dx х — 7 ...

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Q: A Cepheid variable star is a star whose brightness alternately increases and decreases. For a certai...

A: We have to find rate of change of the brightness after t days and 5days

Q: Evaluate the following improper integral. If it diverges, then type 'DNE. Otherwise, find its exact ...

A: ∫10∞56x2-16dx

Q: 3 dx (x2–1)2

A:

Q: Consider the following. 6 x −  1 y = 7 (a)  Find  y ′  by implicit differentiation. y ′ =        (b)...

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Q: The production function for a firm is p(x, y) = 96x*y"4, where x and y are the number of units of la...

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Q: 11. f(x, y) = x' + 2y – xy – 7x

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Q: Find the following for z = f(x, y) = x? +5x2y3-y. az %3D ax

A: FOLLOW NEXT STEP

Q: Consider the table showing past and projected federal revenue, spending, and GDP. All figures are in...

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Q: Directions: Please write your solution on the space provided and boxed your final answer. *Introduct...

A: Topic-  continuity and differentiability 

Q: 12. lim [(x 5) - 3x] isOHOAHOH 3OH2 UA a. lim (x 5) + lim 3x IROCORO b. lim (x- C. X-5- lim 3x X-a -...

A: 12)limx→a[(x-5)-3x] = limx→a(x-5)-limx→a3x13) limx→1x2-2x-3x-2=12-2.1-31-2limx→1x2-2x-3x-2=1-2-3-1li...

Q: Determine whether the series converges, and if so find its sum. Enter the exact answer as improper f...

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Q: 4. Calculate the volume (V) of the following blocks, when given: Length (I) Width (w) Height (h) Vol...

A: see below the answer and calculation

Q: Write the first five terms of the sequence, give the exact answer: +oo n n + 19 n=1 Determine whethe...

A: We have to find first 5 term of sequence and we have to check weather it is convergent and divergent...

Q: Hw. Fin ow for the following functions and du cosh (cot( ) 4- ws

A: Given: (1)  w = 4x4+6x3y2+2x2y3+y4   (2) w  = cosh5cotxy

Q: .y(xy-2)ok+ x(*y+ 2y-지아y - 0 :vi) -1 ' = 0 : y(1) = 1 3.

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Q: 9. cos (21) di 10. 11. sin'x cos's de 12.

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Q: 5. 4. 3 2- -6 -5 -4 -3 -2 -1 -1 3. -2- -3 -4 - -5+

A: Concept - with the help of graph of Tanx

Q: Find the derivative as indicated. 1. y = 3 cos x + 2 sin x ; find y' 2. f (t) = t sin t ; find f' (3...

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Q: 1. A stone is thrown vertically upward from the top of a house 50 ft above the ground with an initia...

A: Due to Bartleby guidelines, only 3 sub parts can be solved. Please repost the remaining questions to...

Q: Given the differential equation у" + 5y' — 14у %3D 7х2 езx sin(&x) Determine the differential operat...

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Q: Solve the following differential equation using appropriate method. 2. (2x + 4y + 6) dx + (4x -2y-5)...

A: The given differential equation is; (2x+4y+6)dx+(4x-2y-5)dy=0