Solve the given ODE using the method of undetermined coefficients. y" – 4y = (x² − 3)(sin2x)

Q: Find the exact value of the surface area generated by revolving the curve 1 + 1≤x≤2, about the…

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Q: Let f(x) = 2x³ - 3x² - 120x+7. a. Find all points on the graph of f(x) at which the tangent line is…

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Q: Question 4 A conical water tank has its top at ground level (consider this to be the x-axis) and its…

A: The given problem is solved below in detail.

Q: Grades - MAC231 X 2311 Section 3.3 X MindTap - Cenga x E CalcChat | Calculo X Mathway | Calcul x b…

A: Topic:-  trigonometry ratios  and derivatives

Q: (a) √738(t - 4)dt (b) 738(t + 2)dt (c) √²38(t+4)dt (d) f²3x²8(t-4)dt (e) ¹3x²8 (t+2)dt -3 (f) ²3x²8…

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Q: 6) INVERSELY LOGARITHMIC The following information is given about a logarithmic function of the form…

A: The objective is to find the rule of the inverse of the function.

Q: Find the area of the region enclosed by the graphs of f(x)=x²-10x and g(x)=6x 50-64

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Q: culate √2-4i. Give your answer in a + bi form. In polar form, use the angle 0 < 2TT.

A: Topic:- complex number algebra

Q: Q4:Evaluate 1) lim (1-²) x-0 \sin x

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Q: 7. Evaluate the volume generated by revolving the area bounded by the given curves using the hollow…

A: The given curves are x=4y-y2, y=x.   Now find the point of intersection between the curves…

Q: A = 15-6 14 53 2, b= 22 12 9 -6

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Q: y = 2sinx and y = 0 from x = T to x = 4 π 2

A: The given curves are y=2sinx and y=0 from x=-π4 to x=π2. So, the bounded region is as shown below;…

Q: B. Graph each equation. 3. 3x²2y² - 12x + 12y = 12 4. x² + 2y² + 2x - 8y = -5

A: Graph of : 3x2 - 2y2 - 12x + 12y = 12

Q: === =+ = ²x² 6 2x Find the arc length given: y = - on the interval [1,2]

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Q: :S- iven : alue of AB 3 8x+1 4x- dx. If we let the substitution" = 4x-5, the final answer takes the…

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Q: The area bounded by y = 2x² - x³, and y=0 is revolved about x=0. Find the volume of the solid…

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Q: (D³ - D² - 4)y = 0

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Q: lim x-0 x - tan x3 X

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Q: A force is specified by the vector F = (155i +80j - 200k) N. Calculate the angles made by F with the…

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Q: Find the antiderivative F(x) of f(x) = 8(sec x)(sec x – 4 tan x).

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Q: An airplane is heading north at an airspeed of 500 km/hr, but there is a wind blowing from the…

A: We have to find the angle and speed of the plane.

Q: Find the volume generated by revolving the area bounded by y = 1 - x³, OX and OY about the x-axis.

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Q: 10. At what rate is the vertex angle of a right circular cone changing when the radius is 3 ft and…

A: The given problem is solved below in detail.

Q: y" - 3y" + 3y' - y = x - 4ex

A: Let's solve diffrential equation.

Q: Problem 2: Use the definition of the Laplace transform to find the transform of the piecewise fu…

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Q: Find the volume of the solid obtained by rotating about the y-axis the region bounded by the curves…

A: Cylindrical shell Method : If th eregion between the two curves y=f(x) and y=g(x) and f(x)≥g(x) is…

Q: 11. Suppose a population grows according to a logistic model with initial population 300 and…

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Q: The area bounded by y=1-x²₁ x+y=1 and the x-axis is submerged vertically in the water with the water…

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Q: A 60-m climbing rope is hanging over the side of a tall cliff. How much work is performed in pulling…

A: We have to find work done.

Q: y = 2 sin 3x 1+3 cos2x

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Q: dy dx + y = 2xy-ex

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Q: Evaluate r5/6 -π/6 2 cos 0 fo² 0 r sin Ødr de.

A: We have to evaluate ∫-π65π6∫02 cos θr sin θ dr dθ.

Q: 2. Given the following logarithmic expression: log, 1+ 2log 5 + log₂ 2 +log, c-log, 100 Which of the…

A: Given: logc1+2logc5+logc2+logcc-12logc100

Q: Find the slope and the equation of the tangent line to the graph of the function at the given value…

A: Topic = Derivative

Q: Problem 2: Use the definition of the Laplace transform to find the transform of the piecewise…

A: Let's find.

Q: 9. y = 3 Arcsec 3x

A: On solving this we will get

Q: dy : Find the for the following functions: dx 1- y = e(x+ln 5x) 2- y = cosh-¹ sin 2x 3- y = xsinh x

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Q: B. The vector = (4, -2, 1) ends at the point P=(7,-7,2). At what point does the vector start?

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Q: 8. y = x ¹ Arctan 4(x4)

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Q: Q4:Evaluate 1) lim (1-²) x-0 \sin x

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Q: Solution: Here f(t) = 24,0 < + <l 0,1 < t <2 Here period of f is 2L = 2 L = 1 ". The Complex Fourier…

A: Given problem:-

Q: 45. 2 (2-x)² √2+x I = (A) 2 √2=x dx = ²√ √/²³ (x) + (B) 1 +c, then f '(1) is equal to - c (C) 4

A: If, I=∫22-x22-x2+x3 dx=34f2x3+c, then to determine the value of f'1.

Q: could you elaborate how to get the missing limits

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Q: . y = 3Arcsin (2x³) -- Arccos(2x³)

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Q: For what values of p does the series p<3 n = 2 1 (n² In(n)) converge? (Enter your answer using…

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Q: 8. Determine whether the series (-1)" is absolutely convergent, conditionally 7n-5 n=1 convergent,…

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Q: Problem 2: Use the definition of the Laplace transform to find the transform of the piecewise…

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Q: dw Q11- express by using the chain rule: dt w = ln(x² + y² + z²) x = cost, y = sint, z = 4√t

A: We have to express dwdtby using the chain rule:

Q: Q3: Fill in the blanks in the following: 1. If a=(3,-2, 6) and b =(4,-1,-6) the axb = ********* 2.…

A: Note: As per our company guidelines we are supposed to answer the first three sub-parts of the…

Q: 3. Evaluate the following integrals. For each integral, briefly explain what method you are using…

A: Please see the answer below.