3. Find the centroid of a thin flat plate covering the region enclosed by the parabolas y = x² − 3 and y = −2x².

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A: Rolles theorm 1) if f( x ) is continuous in [ a,b ]2) if f( x ) is differentiable in ( a, b ) 3) if…

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A: As per guidelines of bartleby we solve only one problem

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A: Hyperbola

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A: Given,            ∫dxx9x2-9

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A: For relative maxima f'( x ) = 0 f''( x ) < 0 g'(x) = - 3x(x + 2) (x - 3)

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A: Please see the below picture for detailed solution.

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Q: 10. Find the horizontal and vertical asymptotes of the curve. 2x² +1 (a) y=- √x*-4 2x²+x-1 x²+x-2…

A: Since you have asked multiple questions in a single request we would be answering only the first…

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Q: Use Integration by Parts to find 2x tan-¹(x) dx. df O r² (tan(x)) — 2(tan-'(x)) +C O r² (tan-¹) +…

A: Integration by parts

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A: We can find the area of the region .

Q: Question 19 Compute the given integral. fre -1² dx = Submit Question > Jump to Answer +C

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Q: Perform the matrix operation. Let A = °[4 4 -3] -16-4] O 0-31 [0-12] O [d [-2 2 -8-8 O -4 -3 0 -12]…

A: Given query is to perform indicated matrix operation.

Q: 1) Let an = 3+2(n-1). Write the first 5 terms of an. Find Σ10% ακ k=1

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Q: convergent serie 12) Find the sum of each 2 A) / + = + ( ² ) ² + ( ² ) ³ + ( ²1 ) 4 + ... ( - )^² +…

A: Let's find sum of given series.

Q: Which of the following would correctly give the area bounded by y = e, y 3x-1 1/³ (e³ª-1 - eª) dx Of…

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