y" + 2y' + 5y = 4e¬t cos 2t, y(0) = 1, y'(0) = 0

Q: Find the derivative of F (x) = S (t3 – t)° dt. O 5( – t)* (3t2 – 1) - O (2 - 2) O 5(x³ – 2)* O 3t2 –…

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Q: |y csc?y dy is equal to A) y coty+ coty B -у соty + coty dy C) None (D -y coty - | coty dy E у coty-…

A: we have to find out

Q: The particular solution that satisfies the differential equation and the initial condition dy/dx =…

A: topic- differential equations

Q: 3x? (x³ + 4)* dæ = 5120 Select one: O True O False

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Q: Consider the following. RX) = x In x², (-1, 0) (a) Find an equation of the tangent line to the graph…

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Q: Find the volume of the solid that is bounded by the surfaces z = = 92 - x2 - y2 in the first octant.…

A: 0≤ z ≤ 81-x2-y2z=0x2+y2=920≤y≤81-x20≤x≤9

Q: Let u = x + 7y and v = x - y. Subtracting v= x - y from u = x + 7y, we get y = Adding u =x + 7y and…

A: Given:      Let u=x+7y              v=x-y Subtracting v=x-y from u=x+7y, we get…

Q: dt, if we let V Vt+1-2, then dt is equal to A (4x³+2)dx B None © 2(x²+2)dx D 4x³dx E 4x(x²+2)dx

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Q: Find the value of n in the following definite integral. So 4x° dx 1 Answer:

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Q: an arithmetic sequence is 75 and the second term is 11 Find the first term.

A: Here I am providing the handwritten solution

Q: Find two positive numbers whose product is 750 and for which the sum of one and 10 times the other…

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Q: Let f(x) = y = 4x² In(). Differentiate y = 4x2 In() with respect to x and simplify. + 4x2 )(()이) -A…

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Q: One of the correct steps to evaluate x2Inx dx to yield the correct integral x³Inx A x² dx 3 O ---fa…

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Q: A farmer finds that if she plants 85 trees per acre, each tree will yield 65 bushels of fruit. She…

A: answer is in next step

Q: S. dx 2. x²V4-x2

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Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. y = -x2 -…

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Q: Find the cost function for the given marginal cost and fixed cost. Marginal Cost Fixed Cost (x = 0)…

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Q: Use the fundamental theorem of calculus to evaluate the following definite integral. | (3x2 + 9) dx…

A: Given query is to find the value of the integral.

Q: help answering

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Q: What trigonometric substitution should be used to evaluate ? A x=3 sec® B x=3 tan0 x= 3sin0 D) None…

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Q: integral

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Q: Refer to the graph below. Find the consumer surplus for the demand function, D, when x= 20. Hint:…

A: We have to find the consumer surplus for the demand

Q: L 3x2 dx = 65 %3D Select one: O True O False 2Vadx = 104/3 Select one: O True O False L (x +4)(2 +3)…

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Q: One of the correct steps to evaluate x2Inx dx to yield the correct integral

A: Our Aim is to identify the correct step to evaluate ∫x2 ln (x) dx to yieldthe correct integral.

Q: Resource allocation. A coffee manufacturer uses Colombian and Brazilian coffee beans to produce two…

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Q: T/3 sin4xdx = 4 T/12 Select one: O True O False

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Q: Find an equation for the hyperbola that satisfies the given conditions Foci: (+5, 0), vertices: (±3,…

A: Given (5,0)=(h+c,k)    hence k = 0(-5,0)=(h-c,k)h+c=5h-c=-52h=0h=0Therefore (h,k)=(0,0)

Q: Find the volume of the solid generated by revolving the region bounded by the graphs of the…

A: Given

Q: Use the indicated substitution to evaluate the integral. • 7/2 dx, x = 7 sin(0) V49 x2 (Give an…

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Q: The particular solution that satisfies the differential equation and the initial condition of dy/dx…

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Q: An antiderivative for is: 22 +81+20 1 O In + C I+8 ㅇ 올tan-1 () +C 금i미플의 O In 28|+ C O tsec- (4) + C

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Q: Find the value of n in the following definite integral. 4x° dx = 1 Answer:

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Q: Use the Root Test to determine convergence or divergence (or state that the test is inconclusive) of…

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Q: x = -3x1 – 2x2 x2 = 9x1 + 3x2 %3D

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Q: S- x³dx is equivalent Vx²-4 Using trigonometric substitution,

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Q: Find the magnitude Iv|| and the direction angle 0 for the given vector v. v= - 7i+ 10j ... (Round to…

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Q: Verify Green's Theorem by evaluating both integrals y2 dx + x² dy = dA ду for the given path. C:…

A: In this question we can verify the Green's Theorem . i.e, ∫C M dx +Ndy = ∫∫R ∂N∂x-∂M∂ydA .

Q: Find the equation of the function f whose graph passes through the point ( 0, and whose derivative…

A: Given :

Q: Use the Limit Comparison Test to determine the convergence or divergence of the series. 1 n Vn8 + 4…

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Q: x³dx is equivalent to Using trigonometric substitution,

A: Given,  ∫ x3x2-4dx

Q: Use Green's Theorem to evaluate the integral. Assume that the curve C'is oriented counterclockwise.…

A: Green's theorem states that for  counterclockwise direction∮CPdx+Qdy=∬R∂P∂y-∂Q∂xdxdy

Q: dP/dt= P(P − 10),

A: answer is in next step

Q: dx 2. x²V4-x?

A: Just use the trigonometrical substitution to make integral easy and then solved it.

Q: du u and dx du Identify u and dx du u" dx Finding for the integral dx.

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Q: 5+a 5 lim, 0

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Q: So 3a (a + 4) dx = 5120 Select one: O True O False

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Q: Use the Derivative of the Inverse Theorem to calculate g'(x), where g is the inverse of f. f(x) x +…

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Q: integral using ir

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Q: x'y" – xy' + y = In(x)

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Q: Use the Fundamental Theorem of Calculus to evaluate the following definite integral. | (4x2 + 9) dx…

A: To find the value of definite integral using  fundamental theorem of calculus.