Use the method of cylindrical shells to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the indicated axis. Give your answer in terms of r. (Type pi for T) 2. y y= 0, x=3, x= 4, the y axis

Q: Find the general indefinite integral. (Use C for the constant of integration.) | (x2 + 2x - 3) dx…

A: The objective of the question is evaluate the indefinite and definite integral.

Q: Evaluate the integral | 3t³ (t² + 4)5dt

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Q: 5. (4x3 — 6ху?) dx + (4y3 — 6ху) dy 3D 0

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Q: After we review on how to solve system of linear equations using algebraic methods (substitution,…

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Q: Let f(x) = 4x^2 – 7x. Use the ɛ/8-definition of the derivative to prove that f'(2) = 9.

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Q: Assume the acceleration of the object is a(t) = -9.8 meters per second. (Neglect air resistance.)…

A: Given data÷ As you have suggested i have solved all steps of part 1.

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Q: 3. Anabelle would like to invite 9 friends to go on a trip but has room for only 5 of them. In how…

A: We can solve this as follows:

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. x = 5 + 3y, 1 <…

A: We have to find the surface area of the solid.

Q: 1. Find particular solution of the following differential equation: dy 15- + 2r-3 dr - 3x-2 =0…

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Q: Evaluate the integral (Trigonometric Substitution) x*dx (x² + 9)2

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Q: a. f(x) = V3x3 – 2 %3D b. y = (Vx + 1)(x² – x) 2x5-3 c. f(x) cos x d. y = sin(4x²)

A: All the questions are solved below.

Q: SOLVE THE EQUATION. SHOW YOUR COMPLETE ANDCLEAN SOLUTION. (x – 2y + 5) dx - [2 (x – 2y) + 9] dy = 0…

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Q: Suppose z is a function of x and y satisfying the equation rey + ye" + ze = 1. Use implicit dz dz…

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Q: Find the volume of the solid that results when the region bounded by y = Vā ,y = 0 and æ = 4 is…

A: Volume

Q: Determine the indefinite integral 6.xV-5]7 dx by substitution. (It is recommended that you check…

A: We have to solve  ∫6·x3·x43-57 dx.

Q: Find an equation of the sphere whose endpoints of a diameter are (−2, 0, 5) and (−1, 2, 3). Show all…

A: Here we have to obtain an equation of the sphere whose endpoints of a diameter are (−2, 0, 5) and…

Q: [- 4,4, – 4] and i = [-5,6, 2] find %3D a. 2u + 47 b. ū • с. п х d. lūl

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Q: 4. Find the integral of your answer in problems 2a and 2b. CO

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Q: Find: d/dt (xe^x)

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Q: 17. у dx — (х + бу?) dy 3D0 (х + бу?) dy %3D 0-

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Q: Evaluate the indefinite integral. 9x xp- x² – 4

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Q: eax sin bx dx

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Q: Two transverse waves y1 = 2 sin(2nt - x) and y2 = 2 sin(2rt - Ix + T/2) are moving in the same…

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Q: 642 1. Consider the graph of y = f(x) below. State the value of each of the followin u do not need…

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Q: 7. Find ſxsec¯'xdx using integration by parts made simple or otherwise.

A: Given ∫x sec-1x dx To find integration

Q: 北13 find the the Value an equation Curve at the Value for the line tangent to Point defined by of t.…

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Q: What is the equation of the given ellipse? YA

A: Vertex ( -3 , 2 ) covertex ( -1 , -1.5 )   Center= ( h , k )= ( -3 , - 1.5 )   Major axis b = 2 - (…

Q: 1 Find Vf(P) and Df(P). (a) f(r,y, z) = y² + 2² – 4x2; U = i – +; P(-2,1,3) %3D |

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Q: Use the chain rule to calculate the first derivative of the following 19. (2x + 6)3 20. In (3x - 2)…

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Q: Suppose z is a function of x and y, and a? – y? = 2"e6y. Solve for dz dx

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Q: Find an equation for the hyperbola that satisfies the given conditions. Vertices: (±1, 0),…

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Q: Consider the graph and determine the open intervals on which the function is increasing and on which…

A: Observe the given graph and decide whether function is increasing or decreasing.

Q: Consider the following series. n In(n) n = 2 Does the function f(x) satisfy the conditions of the…

A: This is a problem related to series and sum calculation. By evaluating integral we will answer the…

Q: Siven that y = f(x) passes through (2, 1) and f'(x) = 3x² - 5x, find f(x). %3D

A: Given query is to find the function

Q: There is a line through the origin that divides the region bounded by the parabola y = 2x – 8x and…

A: There is a line through the origin that divides the region bounded by the parabola y=2x-8x2 and the…

Q: a. Find any intercepts (list as ordered pairs). x-int y-int b. Find any critical numbers. c. List…

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Q: Describe the graph of the equation. r = 19 sin 2t i + 19 cos 2t j O It is a circle of radius 19 in…

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Q: Compute f'(1) where f(x)=1/2 e-2x + ln(x2 + 1)

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Q: 1. Find the value of the directional derivative at the particular point Po for the given function in…

A: Given that gx,y=y2tan2x ; U→=-32 i^+12 j^ ; P0π3,2We need to find the value of the dorectional…

Q: Solve the differential equation. Show your complete and clean solutions. 2 (x-y) dx + dy = 0

A: The given DE is: 2(x-y)dx+dy=0⇒dydx=-2(x-y)⇒dydx=-2x+2y⇒dydx-2y=-2x...(1)

Q: Test the series for convergence or divergence using the Alternating Series Test. 00 (-1)" 3n + 1 n =…

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Q: Find the area of the region. See Examples 1, 2, 3, and 4. f(x) = x2 - 7x + 6 g(x) -x2 + 5x + 6 y 10…

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Q: The multiple choice answers to choose from are A) (lnx)^2 B)2x^(lnx-1) lnx C) x^lnx-1 lnx D) 2lnx/x

A: We can simplify the answer: 2xlnxlnxx=2·xlnxx·lnx=2·xlnx-1·lnx  Because xaxb=xa-b=2xlnx-1lnx

Q: a 0 0 0 0b0 0 11. Using cofactor method, prove that det M = abcd %3D 00c0 0 0 0 d

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Q: dy/dx + 2xy + xy = 0 Ans. 1/y3 = -;+ 1 + ce3x? 2

A: The given differential equation is  dy/dx + 2xy +xy4=0

Q: The point (4, k) lies on the ellipse 32 y? = 1. 18 Which of the following could be a value for k? 0…

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Q: Find the sum by adding each term together. Use the summation capabilities of a graphing utility to…

A: We have to find the sum of the given series.

Q: c) Create a set comprehension for the set F = {1,2,4,8 %3D

A: Solution of the problem as follows

Q: A producer has determined that the revenue generated from the production and sale of x units of a…

A: what interval(s) of production is the revenue increasing and for what interval(s) is it decreasing?