Let an = n> 1. In(2" + 1)' 1. Determine if the sequence {an}1 is convergent or divergent. 2. Determine if the series an is convergent or divergent. Explain briefly. n=1

Q: Given the power series 2 2n A x(n + 3) n = 0 Use the technique that we covered in this unit to Shift…

A: To shift the index of the power series use the substitution n = R - 3

Q: 1. Find the Radius of Convergence (R.O.C.) and the Interval of Convergence (I.O.C.) for the…

A: Consider the power series                 ∑n=1∞ an(x-a)n then series will convergent if x-a<R ,…

Q: Evaluate the definite integral. NOTE: Enter the exact answer. (100,² + 1) – 352 10 ti + t*j dt

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Q: 4. Find an equation of the tangent plane to the surface x = u? + 1, y = v + 1, z = u + v at the…

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Q: Use Gauss-Jordan elimination to solve the system 5x + 7y = -11 2.x + y = 1 Make sure you create the…

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Q: Find the standard form of the question of the ellipse with given characteristics and center at the…

A: This is a problem related to conics section. Based on the general formula and concept we will…

Q: Question For the function f(x) given below, evaluate lim f(x) and lim f(x). X00 X→ー0 f(x) = –3x*…

A: Given that       f(x) = -3x4 .

Q: If cos(0) = 2, and 0 is in Quadrant II, then what is sin (:)? Give an exact answer, using radicals…

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Q: Evaluate the integral / | Vf. dr Vf•dr where f (x,y)=xy² and C is a curve from (1, 1) to (2, 3).

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Q: Consider a triangle ABC like the one below. Suppose that a=14, b=10, and A=82°. (The figure is not…

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Q: The h$(2x) sech (2x) dx is equal to sech (2x) sech (2x) +C. A. 1 3 10 B. None of the choices in the…

A: Solve the following

Q: Solve the equation 6cos?x + 11cos x = -4 given that 0 < x < 2n. Provide your answer below: X =

A: First I have made factor of given trigonometrical equation and then seperetly solved them and find…

Q: Evaluate the indefinite integral. (Use symbolic notation and fractions where needed. Use C for the…

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Q: Σ 2(3n 1) 6n + 4

A: The series is convergentsee below the calculation

Q: 6х — 8г? — 5 dx (2х — 1)(4г? + 1)

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Q: Apply L'Hôpital's Rule to evaluate the following limit. It may be necessary to apply it more than…

A: Solution :let,y=limx→0+cosecxsinxtake log both…

Q: Given the differential equation y' = &r + y2 Find the Implicit derivative " dy/dx" of the…

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Q: Consider a triangle ABC like the one below. Suppose that B=122°, a= 29, and c=59. (The figure is not…

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Q: flx)= x-x 3! %3D 5! 7! f'(x) = 1-x %3D 21 41. 6 ! 2. Drove that

A: fx=x-x33!+x55!-x77!+.......f'x=1-x22!+x44!-x66!+........

Q: Given the differential equation y' = 4x y Find the next two Implicit derivatives of the differential…

A: The given differential equation is y'=4xy ............................................. (1)…

Q: Find the coefficient for x' when |V1+ x° dx is expressed as a power series. -1 256 -1 64 1 56 120…

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Q: Consider a function f(x) whose domain is a < x < b Given the graph of f'(x) answer the following…

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Q: Find the general solution of the given differential equation. x²y' + xy = 2 y(x)%3D

A: This is a problem related to differential equation. Based on the general formula we will answer the…

Q: Find the sum of the convergent series below. Show complete solution

A: This question is related to infinite series, we will solve it using given information.

Q: A thermometer is removed from a room where the temperature is 70° F and is taken outside, where the…

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Q: 1. Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8)); u = i

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Q: Find the area of the region enclosed by the curves x=2y3 – 8y2+6y, x=y2 – y (A) 12.72 в) 13.42 17.32…

A: The graph is shown below:

Q: Find two linearly independent solutions of 2r2y"- xy' + (-4x + 1)y = 0, x > 0 of the form Y1 = r (1+…

A: Given fill in the blanks have already some data, it is wrong as per given question. I solved it, and…

Q: Ex If 3=Nメ+J文 3-(x「x)文 find ý (de)

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Q: Use the first derivative test to find the location of all local extrema in the interval (0, 27) for…

A: answer is in  next step

Q: A tank contains 150 liters of fluid in which 20 grams of salt is dissolved. Brine containing 1 gram…

A: Given that the initial amount of salt = 20 g    and rate of pumping in=3L/min  Let A be the amount…

Q: Sketch the graph of the given polar equations. 5 17. 0 = %3D

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Q: converges

A: We have to determine the given series is converges or diverges

Q: Use L'Hôpital's Rule (possibly more than once) to evaluate the following limit lim (203+922 8x3-8 If…

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Q: A pilot is flying over the ocean. He determines that the angles of depression to two ships are 65°…

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Q: 3. (LO 4 & 5) Suppose we know that: § f(x)dx = 3.5 and g(x)dx = -2.1 Use this information to find:…

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Q: 17495 17.298 Solve these equations for x and k: k(17.00)*= 0.1120 (Hint: divide one equation by the…

A: k(17)x=0.112 →(1)k(30.6)x=0.2016 →(2)dividing both…

Q: Given: 00 (-3)"(x – 2)" n Vn + 2 n=0 Determine the radius and interval of convergence of the power…

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Q: Determine all critical points for the following. Identify the absolute max/min. a) y = 2Vx + 1 - x…

A: As per Bartleby answering guidelines if multiple questions are posted in a single picture then an…

Q: Calculus question

A: Detailed explanation is attached.

Q: dx (x²+1)(x²–2x+1)

A: This is a problem of integration of the function. Please follow the procedure given below.

Q: A particle moves along the x-axis with velocity given by v(t) = 6t2 – 18 for time t > 0. If the…

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Q: Let ū and v are unit vectors such that the angle between them (when joined tail to tail) is 30°,…

A: Find your answer below

Q: dx а. 3 x²(9x² – 4) .2 -

A: The integration of the integral is 1/[x2(9x2-4)3/2].

Q: Given f (x,y) =4e * In y with x = 3x In (u cos t) and y = u sin t. The correct value of dz evaluated…

A: option (B) is correct see below the calculation

Q: Solve the given initial-value problem. xy' + y = e*, y(1) = 8 y(x) = Give the largest interval I…

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Q: dz evaluated at dt 4x If z=tan In with x=sec t and y=e". Then the value of y t= 0 is equal to ...…

A: Given,             z=tanln4x2y with x=sect and y=e2t.To find : The value of dzdt at t=0.

Q: Consider the function f(x, y) = 3x² – 4y² subject to the condition x? + y? = 36. Use Lagrange…

A: Here, the given function is: f(x,y)=3x2-4y2 subject to the constrain g(x,y):x2+y2-36=0...(1)

Q: Identify and sketch the graph of the following equations in R. (a) a2 + 2y? + z2 – 8x + 12y – 2z +…

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Q: = sin? (esin" t) + cos-1(2t3 (x) = tanh-1 x + In V1– x2 |

A: