Solve if the improper integral below diverges or converges. If it converges, solve for the value. 1 et (1 – e*)²

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Q: etermine if the given converges or diverges. Find the value if it converge. | In(x²) dx -1

A: To integrate the given function.

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Q: 8. [sin? x cos' x dx Ssin*

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Q: Find y' if 3x2- (ry?) = 2y.

A: y' = ? 3x2 -(xy2)1/2 = 2y3 3x2 - x1/2y = 2y3 differentiate with respect to x 6x - y/2x - xdy/dx =…

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

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Q: Use the 3rd Degree Maclaurin polynomial for g(x) to approximate the value of 0.2 cos(0.1). = x COS…

A: Here, the given function is: g(x)=x cosx2 Now, we know the series of cos x, the series of cos x is:…

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Q: Consider the function f(x) 5x + 1 (a) Find the Maclaurin series of the function f(x), stating your…

A: Let's find.

Q: Find y' if 3x2- (xy²) = 2y³ 2 3=

A: Given: 3x2-xy212=2y3   As we know that; The sum/difference rule: f±g'=f'±g' The Power law;…

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A: According to our policies we are allowed to solve one question at a time so kindly repost other…

Q: | #(9 – In² x)5/2 dx I. Evaluate the following integrals. 1 1. -d.x x(9 – In? x)5/2

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Q: Evaluate the following integrals. 2x3 – x² + 2x – 2 dx r²(x² – 2x + 2) | | 1.

A: Since you have posted multiple questions which are not interlinked, i can do first question as per…

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: 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: 3) у %3D 2u* + 1 x = 5u? – 5u -

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

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Q: Q4) Find plane area inside the polar function r 2 and outside the polar function sin -0) +1 in first…

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Q: homogeneous

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Q: I. Evaluate the following integrals. 1 1. dx J x(9 – In² x)5/2°

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Q: Recall that e* : 리 for all x€R n: 0 (1.) Find the Maclaurin series for xc * (2.) Use the 2nd de gree…

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