Find a formula for the linear function with a slope of 8 and a y-intercept value of 8. Use x as the independent variable.

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Q: Use the Integral Test to determine whether the infinite series is convergent. n2 Σ n=19 (n³ + 3)7 To...

A: ∑n=19∞n2n3+372We need to find the given series converges or diverges

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A: This question is based on cylindrical shell method integration.

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Q: answer

A: Please refer to the image below

Q: Evaluate the improper integral. 9. 3x²e* dx (Express numbers in exact form. Use symbolic notation an...

A:     ∫-∞9 3x2ex=3·∫-∞9 x2exdx=3x2ex-∫ 2xexdx-∞9=3x2ex-2exx-ex-∞9=195e9

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A: Given that: ∫1x1+x6dx

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A: Given that: ∑k=1∞4k+27k-1

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A: Simple value put

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A: If a function is given as y=f(x), then To shift it up wards by k units we use y=f(x)+k To shift it d...

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A: This question is based on conversion from repeating decimal to fraction.

Q: 4.3 in. 15. Higher Order Thinking A cake has two layers. Each layer is a regular hexagonal prism. A ...

A: Formulas: Area of a hexagon = B=12Pa. Where, P=Perimeter of the hexagon. a=Length of apothem.   Volu...

Q: y" + y' + 7Y e (sin 3x - cos 3x) (undetermined coefficients)

A: Given

Q: Evaluate the indefinite integral. cos x tan³ x dx 3

A:    ∫cosxtan3xdx=∫1-cos2xsinxcos2xdxLet  u=cosx=∫ -1-u2u2du=∫ -1u2+1du=-∫1u2du+∫ 1du=--1u+uSubstitute...

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Q: Evaluate the integral. Show all your work. dx (x² – 1)3/2

A: Given that: ∫dx(x2-1)3/2

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A: We can find the exact length of the curve as below,  

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Q: 1. Find the length of the curve r(t) = (sin 2t, cos! cos 2t) from t =0 to t 2n. %3D II

A: 1)- Given: r→t=sin 2t, cos 2t from t=0 to t=2π. The objective is to determine the length of the curv...

Q: 4. y=ysin 2xcos 5x + 3

A: Find your answer below 

Q: Use any method to determine if the series converges or diverges. Give reasons for your answer. 00 12...

A: Given query is to find series converges or diverges.

Q: 6. The limit of that constant is that constant. 7. The limit of a constantc times a function is equa...

A: Since we are given with the multiple number of questions and our guideline is solve the problem only...

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A: Let's find. 

Q: Calculate SN given by Simpson's Rule for the value of N = 6. dx x4 + 8 (Round your answer to five de...

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Q: 20 Find the Maclaurin series for f(x) = - 1+x 20 What is the Maclaurin series of 1+x 00 Σ | (Type an...

A: We have to find the Maclaurin series for f(x)=201+x.

Q: Rewrite the integral in the 5 other orders. Explain your answers. 2 4-y2 f(x, y, z) dz dy dx

A: The given integral is ∫x=0x=1∫y=2xy=2∫z=0z=4-y2fx,y,z dzdydx. The domain of integral is R=x,y,z: 0≤x...

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Q: Determine convergence or divergence by any method. 00 (-1)"n n=0 Vn2 + 9 The series diverges. conver...

A: The given series,       ∑n=0∞(-1)nnn2+9

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A: Calculus  mathematics sequence 

Q: 4) Determine if each of the following series is convergent or divergent. (a) En=1 n4" n-1 Inn (b) En...

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Q: ydx + x(Inx - lIny - 1) dy = 0, when x = 1, y = e %3D

A: Given :     ydx+xlnx-lny-1dy=0,        when x = 1 , y = e that means y1=e

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Q: 6. у3 2x – Jx² – 1

A: Given function y=12x-x2-1 we want to derivative of given function with respect to x 

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Q: use implicit differentiation to find

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Q: Integrals of the form sin mx cos nx dx sin mx sin nx dx cos mx cos nx dx can be found using the foll...

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Q: 4) Determine whether the integral converges or diverges, and if it converges, find its value. - dx (...

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