Evaluate the limit. Select the correct answer below: O + O-3 03 0-1/3/2 0 1/1/012 The limit does not exist. x+1 lim x-3 x² - 2x - 3

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A: Topic:- differential equations Note :- as per our guideline if more than one question uploaded than…

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Q: I. Perform the indicated multiplication on the differential operator D. (D+2x)(D-3x)

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Q: Question 9. A circular helix in ryz-space has the following parametric equations, where ER. I(0) = 4…

A: Given : x(θ)=4 cosθy(θ)=4sinθz(θ)=3θ

Q: 10. Find a Maclaurin series which represents cos(x) for every real number around the point a = 0.

A: As we know the Maclaurin series;  fx=fa+f'a1!x-a+f''a2!x-a2+f'''a3!x-a3+fiva4!x-a4..... Where…

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A: As per the rules, we can answer only the first question and other can be reposted.

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A: Given: I=∫x33x4+23dx     ...1   As we know that; The Power Rule: ∫xndx=xn+1n+1+C ; n≠-1

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Q: II. Solve each of the given LDE of order n. 2. (D³ +6D³ +2D² - 27D+18)y=0

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Q: Please

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Q: 7. Convert the angle 5л 3 into degrees.

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A: Given :fx,y=6x2-2x3+3y2+6xy

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A: Given, S(t)=60t2t2+150

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Q: Given f(x)=√x and g(x)=x²-1, evaluate each expression. (a) f(g(1)) (b) g((1)) (c) g((o))

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Q: 5. What is the domain of the function h(x)= 11 X x 2 1 ?

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A: answer is in next step. please give a like !!

Q: 2. Integrate using an appropriate method. 1 PVR-36° dr

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Q: Solve the problem. 10) Maximize Q = xy2, where x and y are positive numbers, such that x + y2 = 5.

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Q: 5. The tank shown below is full of water. Find the work required to pump the water out of the spout.…

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Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. x³ (3x4 + 2)³…

A: We need to integrate ∫x33x4+23dxSubstitute 3x4+2=tDifferentiate w.r.t t12x3dx=dtNow∫112t3dt ---{1}

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Q: 10. Solve 3log x= log 512-log 8

A: To slove 3logx=log512-log8

Q: 3. State the remainder when f(x) = 2x² −x³ +1 is divided by (x+1).

A: We can find the remainder as below.