Given the series 8" n=1 ant1 find the ratio an (Express numbers in exact form. Use symbolic notation and fractions where needed.) an+1 %3D 00 an Incorrect Use the Ratio Test to determine the correct statement. The series diverges. The Ratio Test is inconclusive. The series converges. 8.

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A: First we take log both sides and then differentiate both sides with respect to x.

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Q: S 12x²Vx3 + 7dx

A: This question can be solved using the concept of integration by substitution.

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A: As per the guidelines when multiple question are posted in single pic  then we are supposed to solve...

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A: Here, the given integral is: I=∫0πsin2x2cos7x2dx Substitute x2=t⇒x=2t⇒dx=2dt as x→0⇒t→0 & as x→π...

Q: Work Problems a) Evaluate the integral (4x + 1) ln x dx b) Evaluate the integral fou | 6 tan" x sec“...

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Q: Replace ? with an expression that will make the equation valid. d 1 In (x8 +9) : %D dx 8 x° +9- The ...

A: Given query is to find the derivative of the expression.

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A: Since, the student has clearly mentioned to solve question number (3), so we are solving only questi...

Q: If f(x) = (2x + 8)-', find f'(x). Find f'(2).

A: topic - derivative of a function

Q: 18) rind fue indefinite inpagrel by ma uing tue Subs titel fion x=2Seco. af -de

A: The detailed solution is given below Thank you 

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A: A) limx-2 (2x2-5x+2)/(3x-6). B)limx-infinity(x2 (3x-1))/(50+4x-2x3)

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Q: IV. Exercises: Find y', y", y'", and y"" for the following expressions: 1. y = x* 2. y = 2x2 + 3x - ...

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A: Here we can solve the integration as below

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Q: Evaluate the following integrals (x2 — х)2 dx 1. x3

A: To evaluate: ∫(x2-x)2x3dx

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

Q: (x – 2)2 +1 if x 2

A: We have to check continuity of function at x=0 and x=2

Q: 1. Evaluate the integral JS aA, where R is the region: {(x,y)|0 < x < 1, –3 < y< 3] x²+1

A: To evaluate the integral: ∫∫Rxy2x2+1dA where R is the region (x,y)|0≤x≤1,-3≤y≤3.

Q: 2sin x -1 2. y = cosx+ 2

A: Since you have posted multiple questions i can do first question as per our company guidelines pleas...

Q: 3. Use the Comparison Test to determine if the series 5n Cos 2n n³ + n² + 1 n=1 converges or diverge...

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Q: Let g(x,y) = x³ – 6x² – y* + 5. Find and classify the critical point(s) of g.

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Q: Find (and simplify) the equation of the tangent line to the graph of

A: Equation of Tangent line to curve y=3xx-1, at x=2

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Q: Find the indefinie intgrel wite 5 sec (2x) tan (2x) dx

A: Topic = Integration

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Q: Use an appropriate test to determine whether the series given below converges or diverges. 00 2n Σ 7...

A: We can test the convergence as below.

Q: True or False: In the partial fraction decomposition, A D + x + 3 x + 8 В x(х — 1)(х + 3) х — 1 - we...

A: (x+8)/x(x-1)(x+3) = A/(x-1) + B/(x+3)+D/x A(x+3)(x) + B(x-1)(x) + D(x-1)(x+3) Ax2 + 3Ax + Bx2 -Bx + ...

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Q: 2) Let r(t) = (t, t² , e'). Find an equation for the unit tangent vector T(t).

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Q: 2. Use the sum and difference formulas to evaluate the following. 5TT COS 12 sin (-) 7Tt а. b. 12

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Q: 5. S(5 -5°dx

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Q: Given Cost and Revenue functions C(q)=q^3-8q^2+52q+5000 and R(q)=−3q^2+2500q​, what costs should t...

A: The given question has been solved in detail.