> (atan (2n – 1) – atan (2n +3)) n=0

Q: The region R is bounded by the curve with equation y = sin 2x, the x-axis and the lines TT x = 0 and…

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Q: Q2) Solve the D.E xdy + (2y – xª + 3x)dx = 0

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

Q: 1 III. Consider an 1 for n eN = {1, 2, 3, ...}. 2n + 1 2n + 3 Find a general formula for the kth…

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Q: бх — 8г2 — 5 dx (2л — 1)(4г2 + 1) -

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Q: 7. y = y5 +6y* +35x³ –5x² –100 8) y= /2x

A: We have to find the 3rd derivative of given functions.

Q: Is the vector projection of B onto A, perpendicular to B? Is the angle between projAB and the vector…

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Q: (cos2y — Зx? у?)dx + (сos2y — 2xsin2y — 2x3y)dy %3D0 - |

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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: Calculate the derivative of the function xe" at the point x = 0 %3D O 1 e O 2e

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Q: 4x + 1 dx Jx3 + 3x2 - 6х -36 2.

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Q: du 2. f 1-cos? 2u

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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: A. LIMITS Limr - 25 1.) lim VE – 2 2.):-4t-4 x-5 x-5

A: Here we have to find the limits.

Q: Solve for the general solution of the following differential equation and determine whether it is…

A: Note : As per our guidelines we are supposed to answer only one question if there are multiple…

Q: Evaluate the integral 2x 4)

A: ∫1e2x-452dx=∫1ex2-452dxSubstitute…

Q: ] Using the alternating test, determine whether it converges or diverges

A: Answer and explanation is given below...

Q: 4 En=1 3 3n

A: The summation of 4/(3n-n1/3) , n from 1 to infinity.

Q: 4 xp£

A: We have to find the integral.

Q: II. Consider the sequence (n + 2)! n=1 a.) Show that the given sequence is monotone. b.) Use the…

A: Given

Q: derivative of f(x, y, z) = x + z at P(6,5,-5) in the direction from P to Q(5,7, -4). NOTE: Enter the…

A: We can solve this as follows:

Q: Solution of lim (Vx² +1 – x) is ... x→ 00 Tentukan lim (vx² + 1 – x) x→00 1. O 1 2. O infinite 3. O…

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Q: Determine whether the following series is convergent or divergent full solution pls and write what…

A: Let's find.

Q: Determine if the improper integral converges or diverges. If it converges, find its value. In dx

A: Here we have to integrate the given problem.

Q: Suppose f(x) is a function that satisfies the following conditions: f(15) = 20, f' (15) = 2. Also…

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Q: V3 3 9) 9 +x2

A: The given integral,        ∫0339+x2dx

Q: (b) S 3x5V1 – 2x³dx -

A: Given,              ∫3x51-2x3dx

Q: vhether the following series is convergent or diverger (-1)"3n² 4n²–1 (b) n=1

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Q: Sketch the region in the plane consisting of points whose polar coordinates satsfy the given condi-…

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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

Q: Find the particular solution of: ydx – 4dy = x²dy when x = 4 and y = 1 |

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Q: Q2) Solve the D.E xdy + (2y – xª + 3x)dx = 0

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Q: Is the function continuous on the interval (0, T COS x O no O yes O cannot be determined

A: Given problem:- Is the function ex/cosx continuous on the interval [0, π] ?

Q: 5. What are the coordinates of the centroid of the area bounded by y = x² +2, x-axis (ory = 0), x =…

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Q: 9.) S(5t + 2t2 - 5t - 50)dt

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: 2n + 1 n=1

A: We have to check sequence convergence.

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

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Q: an = In(n+1) – In(n) for n E N determine if the following is convergent or divergent Σ an n=1

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Q: Using the squeeze theorem, find the value of lim,0 x² sin=) O 1 O -1 O does not exist

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Q: +00 (4-х)^/п+5 4. Consider the power series 9n-7n n=1 а. Use Limit Comparison Test to show that the…

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Q: 1. Sketch the region enclosed by the given curves: y = e*, y = x² – 1, x = -1, x = 1. Find the area…

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Q: ´ax²-3 -, x > 1 х-1 Value of a and b that will make f (x) = continuous everywhere are .. (bx +2,x <…

A: To find the values of a and b that will make the function continuous everywhere.

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

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Q: I. Evaluate the following integrals. 1. / 20- dx 2 x)5/2" x(9 – In².

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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: Find the value of 7x²e-3 Determine whether ) (7n’e- ) n=1 Enter C if series is convergent, D if…

A: Let's find.

Q: Find the derivative. f(x) = 2^x {ln[cot(x)]}^2

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Q: the Q2, Find hergth of o polor Curve ア= B4 Use this formula dr de

A: Given:  The polar curve is given byr=eθ2 To Find:  To find the length of the given polar curve by…

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: (x – y)dx + xdy = 0. (x – 2y)dr + xdy = 0. (x² – y?)dx + 2xrydy = 0.

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