4 5x2 Evaluate dx. TV3x2-1

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Q: п(х-2)" Consider the power series 3" (2п-1)3 n=1 Show that the power series converges when x = 5.…

A: the given series is n(x-2)n/[3n(2n-1)3].

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Q: JVVy+1-2 dy can be evaluated conveniently if we let x =VVy+1 - 2 and dy = 4x(x² +2)dx. (A True B)…

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Q: Show clear and detailed solutions • Determine and draw the graph of the following equation in R3 :…

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Q: 2- cusx dx COSX Sinx +2 Sinx t5

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Q: Calculus

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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: Given: Em 00 tanm tan m+1) q. Find the Sum of this Convergent series.

A: Given that ∑m=1∞1tan-1m-1tan-1m+1Solution…

Q: Find all values of x and y such that Py(x,y) = 0 and Py(x,y) = 0 simultaneously. P(x.y) = 2x2 - 4xy…

A: Topic = Derivative

Q: The task is to evaluate the function using reversed order of integration. •1 eee-x dx dy 1 Jlny

A: Change of order.

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: +o0 In(tan -1 x) dx 1+x2 1

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Q: In(arctan(x)) da 1+ x² 1

A: Given that a integration and we solve this integration by using general formula of integration.…

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Q: pln e" sec? e" dx In 플 Find (a).

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Q: 4. sin x dx 2.

A: Solving question number 4

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

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Q: Find the Maclaurin series of the function. f(x) = 9 cos 2TX 2 (Type an expression using n and x as…

A: We know that the Maclaurin series of the function f(x) is given by f(x) = f(0) + f'(0)1!x +…

Q: 1.5 (3-x QI) Evaluate the integral dy dx using polar coordinate

A: Solving

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A: Note:As per our guidelines we are supposed to answer only 3 subparts if there are multiple subpart…

Q: Write each complex number in complex polar notation: 21) - 4.053 +2.042.

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Q: Reverse order, then integrate SaE ) dydx. Vx \1+

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A: We have to find area bounded by the given curve.

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

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Q: Consider the following Maclaurin series: (-1)"x²n (2n)! cos x = for all x E R. n=0 1. Let f(x) =…

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

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Q: 1 In solving the antiderivative of f(x) 2-3sin(x) by miscellaneous substitution, the substitution…

A: Given problem:-

Q: -+inf In(tan¯1x) 1+x2 1

A: ∫1∞ln(arctan(x)1+x2dxSubstiute u=arctan(x)→dudx=11+x2→dx=(x2+1)du=∫ln(u)duIntegrate by parts…

Q: [ sec" x (Vtan' x+ 1) +1) dx 2. 4 sec'x 3

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Q: Find the length of the polar curve r=2cos(theta) 0 < theta < pi

A: Given:         r = 2 cos θ        0 &lt;  θ &lt; π

Q: Determine whether the following series is convergent or divergent 3- Vn (a) 2 n=1

A: The given series is: ∑n=1∞3-n4n34,an=3-n4n34, n≥1f(x)=3-n4n34

Q: Convert dzdydx Into an integral of spherical coordinates 6coso S6 SR psinødpdød0 psinødpdøde Option…

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Q: 220° 12 сm 70° X =

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Q: dy Which of the following is the general solution of the separable equation, = = 2y - 1? dx in 2y-1|…

A: Solving the problem by finding the differential equation. Here we take C as integral constant.

Q: (-1)"-1"

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Q: ********** . ...... Analyze and sketch a graph of the function. Find any intercepts, relative…

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Q: In(arctan(x)) dx 1 + x2 1

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Q: Example 7 Sketch the curves (c) r 0 (0 > 0) in polar coordinates.

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Q: Integral Calculus: Trigonometric Function (3

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

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Q: Determine if the improper integral (1 e" )2 dx converges or diverges. If it converges, find its…

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

A: Answer and explanation is given below...

Q: Given the following heat equation and the boundary and initial conditions, и, 3 би,и, и(0,1) 3…

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Q: 6a2 + 23.x – 9 The antiderivative of f (a) = is F (x) = a ln (æ + 3|) + bln (lal) +d In (r – 1|) +C…

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Q: homogeneous

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Q: O Fnd the pemainders when @ x³ - 2xx +5x +8 is divided by x-2, (b) x+ x -9 s OC +1 dwided by is…

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