Integrate each of the following functions using substitution, finding the most general antiderivative. Also enter u, the function of x that you substitute. If your answer requires a constant of integration, enter it as c. [5x²¹ √x³ + 2 dx_ a. U = X

Q: Draw the region whose area is given by the definite integral. 9 So (x+3) dx so 5 Which graph shows…

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Q: Find the limit (if it exists) of limx->3+ (3-x)/|3-x|

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Q: Question 7 (D³-4D²y = 5, Find Yp a. 5x² 4 O b. 5.x² 4 OC. 5.x² 12 O d. 5.x² 12 e. none

A: Ode

Q: Calculate the arc length of y = 4x + 1 as a varies from 0 to 2. 8 =

A: As we know that arc length = ∫ab1 + ( dydx )2dxGiven y = 4x + 1 varies from 0 to 2

Q: 7. Convert the points from polar to rectangular. Plot all points on the same graph and label each…

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Q: Set up an integral that represents the arc length of the function y = 4x4 + 4x from the point (-2,…

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Q: Our goal is to estimate the rate of change of d(t) at precisely the time t = 3 se This will be…

A: Given: dt=61.490-t

Q: Find the roots of (D4 + 4y = 0 O a. +2i, ±2i + 2 O b. 2+2i, ti Oclti, -1+i O d.-1 +1, 2+2i O e. none

A: To find the roots of D4+4y=0

Q: = = √²* (t²³ + 5t² + 4) dt 0 If f(x)= then f''(x) =

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Q: A lifeguard needs to rope off a rectangular swimming area in front of Long Lake​ Beach, using 1100yd…

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Q: Given a = log7 5 and b = log, 4, use logarithmic properties to represent each of the following…

A: Given that a=log75 and b=log74, using logarithm properties to represent each of the given function…

Q: Evaluate the integral. 3 1₁²₁x² +2 (x² + 2x - 5) dx

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Q: Use the ratio test to determine if the series converges or diverges n 3+2n n In(n) Σ - n=2

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Q: Suppose that f(x) and g(x) are given by the power series f(x) = 4+2x+ 2x² + 3x³ +... and g(x) = 6 +…

A: We need to find coefficients. As per Bartleby guideline we can solve one question. Please upload…

Q: The total cost (in dollars) to produce q items is C (g) dollars. The marginal cost of producing q…

A: Cost

Q: B. Eliminate the arbitrary constants in the equation y = C₁e²x+c₂e³ +6e". Use (a) elimination method…

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Q: 10. dy_x²-3y² 2xy dx

A: 10. dydx = x2 - 3y22xyit is homogeneous equation with degree 2

Q: Consider the series n=1 (3x)" n Find the interval of convergence of this power series by first using…

A: Radius of convergence of the series, ∑n=1∞anxn  is given by, R=limn->∞anan+1

Q: Find the values of c such that the area of the region bounded by the parabolas  y = 16x2 − c2 and y…

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Q: (D³ - 4D²)y = 5, Find Yp 5x2 4 a. O b. 5x² 4 O C. 5x² 12 O d. 5x² 12 e none

A: According to question,Given Differential equation,D3 - 4D2y = 5

Q: Evaluate the indefinite integral. 5 sin³ (2) cos(x)dx = +C

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Q: In a certain city the temperature (in °F) hours after 9 AM was modeled by the function T(t) = 50+ 14…

A: GivenT(t)=50+14sinπt12 We are required to find the average temperature during the period from 9 AM…

Q: (D³-2D²-5D+6)y=e³x, Find Yp O a. 1 10 O b. OC. xe O d. xe 1 10 3.x 3x 10 10 e. none 3x 3x

A:

Q: (D3-5D2+8D-4)y= 2x, Find Y = Yc - Yp 1 a. O b. c+ciải tế giớ OC 12²³x²= + 12²x²5+ [²³²] + x³²50 -2x…

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Q: Find the indefinite integral. (Use C for the constant of integration.) √x²ex/2 dx

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Q: Evaluate the surface integral. J[ ² S is the surface x = y + 3z², 0 ≤ y ≤ 1,0 ≤ z ≤ 5 z dS

A: Here we have to evaluate the given surface integral where S is the surface x=y+3z2 , 0<=y<=1,…

Q: (15) Determine whether each integral is convergent or divergent. Evaluate those that are convergent.…

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Q: 4. (x² + y2)dx + 2xydy

A: To solve the given differential equation

Q: Find the area under the given curve over the indicated interval. y = 2x; [2, 6] The area under the…

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Q: (D4-1)y= sinx, Find Yp O a. O b. 1 1 10 - sin2x 15 O c. 1 10 -sin2x -cos2x O d. 1 15 O e. none…

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Q: 6.2 7.2 6.8 5.6 5.0 4.8 4.8

A: Given pool, The widths (in meters) of a kidney-shaped swimming pool were measured at 2-meter…

Q: (D2 - 3D + 2)y=e5x, Find Y = Yc + Yp O a. 0³C₁² +₂²² +2² 1 2x 5x Cet 12 O b. О с. c₁₂e-² + C₂e-²x₁ O…

A: We have to solve differential equation (D2 - 3D + 2)y = e5x We have to find  Y = Yc + Yp

Q: Find the mass of a ball of radius 7 if the mass density of the sphere is proportional to the square…

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Q: Find the maximum area of a rectangle that is inside of the triangle formed by the x-axis and the…

A: NOTE: Refresh your page if you can't see any equations. . as we can see from the graph, width and…

Q: A particular computing company finds that its weekly​ profit, in​ dollars, from the production and…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: Determine whether the series below is a geometric series, a p-series, an alternating series, or none…

A: According to question,Given series,∑n=1∞ 2nn4

Q: Question Use properties of the indefinite integral to express the following integral in terms of…

A: To solve the following problem of Integration

Q: (D3-2D2-5D +6)y=e4x, Find Yp a. 1 O 24 O b. 1 0 1 6 O d. 4x 1 4x 18 O e. none 4x e

A: To find the particular integral of given differential equation

Q: Evaluate the definite integral .9 10x² +9 dr

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Q: C. Verify by substitution that each given function is a solution of the given differential equation.…

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Q: Recall the following indefinite integrals for basic proper rational functions, where a and b are…

A: according to bartleby guide line we do only first part ofmultiple please re post other parts a)…

Q: -5<x<0 0≤* <1, then 1≤z<5 0, If f is the Fourier series of g(x)=9x, (11, f(x) =+ Σ[0) 0 (™™ +) +…

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Q: (D3 - 4D²)y = 5, Find Yp 5x2 4 a. b. 5x² 4 C. 5x² 12 d. 5x² 12 e. none

A: Given that         (D3 - 4D2)y = 5

Q: Determine which of the following tests would be best to use to determine the convergence of the…

A: NOTE: Refresh your page if you can't see any equations. . use the comparison test

Q: (D3-4D2)y = 5, Find Yp O a. 5x² 4 O b. 5x² 4 O C. 5x² 12 O d. 5x² 12 O e. none

A: To find Yp

Q: Find f"(x). 13. f(x) = x² + fr) - r³ 375

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

Q: The midpoint of AB is at (3, 4). If A = (7, 6), find B. B is:

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Q: (D2 - 3D + 2)y=e5x, Find Y = Yc+ Yp O a. 1 5x ¨°C et + C₂e²t. + O b. -X ce c₁₂e-x + c₂e-²x + OC. O…

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Q: Equation Find the complete y" - 2y +y = ex X solution of the Differential using Method Variation 어…

A: Please see the below picture for detailed solution.

Q: 5 Which of the following is the standard equation of the ellipse with vertices at (1, 0) and (27, 0)…

A: To find the standard equation of the ellipse