Find the volume of the solid obtained by rotating the region bounded by the given curve about the specified line. y = e^−x,y = 1, x = 2; about y = 2

Q: 2. Simple Chemical Conversion Radium decomposed at a rate proportional to the quality of radium…

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Q: HOMOGENOUS LINEAR DIFFERENTIAL EQUATIONS. (D^3 – 2D + 4)y = 0 ; y = –2 , Dy = 8, D^2y = 0, when x =…

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Q: May I ask why there is a plus 8 in the final answer?

A: We have to explain why there is 8 in final answer.

Q: Evaluate: L-¹{. S-2 (s+ 2)² - 49 4 Â) e-2t(cosh7t - -sinh 7t) 4 B e²t(cosh7t + sinh 7t) (C) e2t…

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Q: Find the derivative of the parametrically defined curve (t) = 2 cos(4t), y(t) = sin(4t). dz 4cos4t…

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Q: 2. Find the general solution of xdy + (3xy + y - e-3x) dx = 0

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Q: Q3/ Find a volume for the region bounded by 4/X and Y = (X-3)² about the x-axis.

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Q: 7. Which of the following is the differential equation satisfied by the given by the particular…

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Q: Using the method of undetermined coefficients, the modified form of a particular solution for the…

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Q: Let L(z) be the linearization of f(x) = sin x + 1 at the point x = . Find L(1/2). O -1 pi/2-1…

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Q: (a) Find the point of intersection of the tangent lines to the curve r(t) = (2 sin(at), 3 sin(at), 5…

A: We have to find equation of tangent.

Q: Initially 80 grams of radioactive substance was present. After 4 hours the mass had decreased by 6%.…

A: Let's find amount remaining after 40 hours.

Q: The expanded form of the differential operator D(xD-1) is A XD²+1 B XD² C XD²-1 (D) XD²-D

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Q: . The implicit solution for the differential equation y' = x³y is A. In x = y² + c B. 3 lnx = y² + c…

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Q: B/Find the oblique asymptote of the function f(x) -3x²+2

A: The function is f(x)=-3x2+2x-1

Q: Find the absolute maximum and minimum values of the function, subject to the given constraints.…

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Q: The general solution of (D³+4D)y=0 is Ay=ex(c₁cos2x+c₂sin2x) B y=c₁+c₂cos2x+c3sin2x Ⓒy=c₁ex+c₂e²x +…

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Q: 7. The particular solution of (D³ - 5D + 4)y = 0, when x = 0, y = -2, y' = 8, y" = 0

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Q: Find L(te²t sin 3t) 2t

A: Given:       Lte2tsin3t  Use Laplace transform table:          Ltkft=-1kdkdskLft For te2tsin3t:…

Q: Which of the following represents the volume of the solid generated by revolving the region bounded…

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Q: General solution of dy dx = tan²(x + y) dx

A: This question can be solved by taking x+y=t

Q: 3x+ +4x +4y² = 25x³

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

Q: The hyperbolic paraboloid (saddle) f(x, y) = x² - y² + 4 is shown in the 3D model below. Find the…

A: Here, to find the volume f(x,y)=x2-y2+4 between the rectangle R=[-2,4]×[-1,2]

Q: dx 2 X - 25

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Q: The Maximum point of y = 9-x² x²-4

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Q: 2. lim x sin(1/x) X18 ex+2x 3. lim X18 ex

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Q: Let f be a function such that -² ≤ f(x) ≤ x² for all x ER. Show that f is differentiable at x = 0…

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Q: Sx [x²cox dx U. V x² Sax - S(α (x²) [ cond) dx dx x² (sinx) - -S 2x Sinx dx U. V. x² sinx - [2x…

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Q: How far does the car travel during that time? * Onone of the choices O260.133 ft O 300 ft O258.133…

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Q: Find the derivative 4cos4t sin4t O2cot4t O Other: -1/2 cot4t of the parametrically defined curve (t)…

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Q: (c) (d) sin 3x lim z0 tan 3r lim (In(sin 2x) - In(tanz)) +0+z

A: Here we have to solve the given limits.

Q: Use implicit differentiation to determine the derivative of the following functions. 1. 3x²+2y²-81…

A: Given :3x2+2y2-81=05x2+4y=16

Q: 5. The auxiliary equation of the differential equation (4D³ - 13D + 6)y = 0 falls under_ Prove your…

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Q: (j) [e³ sin 2rdr

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Q: 3 [²(x²) dx 0 Using the definition of definite integral, ff(x)dx= lim f(x) Ax, and the given…

A: Given, ∫03x2dx

Q: Evaluate the double integral [[ cos(x + y) dA, where R is the region bounded by the lines y = r and…

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Q: A certain tank of depth 10 ft is a surface of revolution formed by rotating y = x² about its axis.…

A: Given : tank depth = 10ft And eqn y=x^2 Find work done?  Formula used : work done = mgh

Q: (D³ - 5D + 4)y = 0, when x = 0, y = -2, y' = 8, y" = 0

A: The given differential equation is: D3-5D+4y=0 when x=0, y=-2, y'=8, y''=0.

Q: A solution of a differential equation free from arbitrary constants obtained from the general…

A: The complete Solution of an Ordinary differential equation is composed of a general solution and a…

Q: 5. Givenz уг у -4x , Find дz ду дz ?x

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Q: If f(x) = A B D tanx S™ 0 1+tan²x 1+etanx sec ³x l+etanx In (secx)√1+tan²x 1+etanx sec²x tanx 1+12…

A: Using the Leibnitz rule:

Q: 26. (2xy2-3x²)dx + (x² + 2y)dy = 0 A. Exact B. Not Exact

A: As, the student has posted multiple questions but we can solve one question at a time according to…

Q: Question 2 Given a differential equation as d²y dy 2². - -3x- +3y=0. dx² dx By using substitution of…

A: Let's solve diffrential equation by using substitution x=e^t  or t=ln(x).

Q: For questions no. 4 and 5. Given: Radium decomposed at a rate proportional to the quality of radium…

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Q: 6. Find a²z дгу of z = In(xy)

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Q: Find Laplace 2 2 [sin(34) + 65inh czt) ]

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Q: Find the volume of solid generated by revolving the region bounded by f(x) = x² + 1and…

A: The functions are f(x)=x2+1 and g(x)=-x2+2x+5

Q: Solve for the area of the region bounded by x² = 4y + 4 and x = y = 2 (A) none of the choices 128 B…

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Q: To evaluate the integral sin³0cos ede by trigonometric transformation, we use the identity; A sine…

A: On solving this we will get  To evaluate the given integral we use the the identity in given option…

Q: 2. Simple Chemical Conversion Radium decomposed at a rate proportional to the quality of radium…

A: Let's find time taken 1/2 the original amount of radium to decompose.