and the net is decribed by the equation y = V1 – x2 – z2, y 2 0,

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Q: x + 4 dx (x² + 2)(x² + 1)2

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Q: Find the arc length L of the graph of r(t). r(t) = 2 cos(t)i + 2 sin(t)j + tk, 0<t< 2n L =

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Q: Find the volumes of the solids generated by revolving the regions bounded by the graphs of the…

A: Draw the region and use the washer method of finding the volume of revolution of solids.

Q: 2. Write the given (total) area as an integral. (vde a. The area above the x- axis and below y = 4–…

A: Here we have to find the area.

Q: Evaluate the integral COS nx dx

A: To solve the integral we use integral by parts formula. From integral by parts formula we get: ∫uv…

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

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Q: Determine whether the series is convergent or divergent. If it is convergent, find its sum. (If the…

A: We have to find if the series converges or diverges.

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: 3 a. f(x) = V3x³ – 2 - b. y = (vx + 1)(x² – x) 2x5-3 c. f (x) coS x

A: a) fx=3x3-23b) y=x+1x2-xc) fx=2x5-3cosx Note:   Multiple parts are given, we are answer only three…

Q: If f(x)=-(x² – 4), find (a) The x-intercept and the y-intercept (b) The interval where the function…

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Q: Jse one of the formulas below to find the area under one arch of the cycloid x = t – sin(t), y = 1 –…

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Q: An elastic band is hung on a hook and a mass is hung on the lower end of the band. When the mass is…

A:

Q: Evaluate the integral -2x + 4 dx J (x² + 1)(x – 1)

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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: Find the maximum and minimum values of the radius of curvature for r(t) = ⟨cost,sin t,sin t⟩, if 0 ≤…

A:

Q: 1 6. Find dx. V2x2 –8x+2

A: Solving

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A:

Q: Determine whether the diff eq. is exact. If it is, find the general solution.

A:

Q: .4 dx (x² + 9)2

A: To evaluate the following integral.∫x4 dxx2+92

Q: 1 dx x+2

A: Given that a integration and we solve this integration by using general property of integration.…

Q: Solve the two items using Integration by parts. 1. (x' V9-x? dx

A: Question - 1:- Given: ∫x39-x2dx Formulas used: ddxxn=nxn-1ddxconstant=0ddxfgx=f'gx·g'x        Chain…

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A: A detailed solution is given below

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A: The given function f(x)=-x2-43

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: Use Green's Theorem to evaluate F. dr. (Check the orientation of the curve before applying the…

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Q: An ellipse has centre (0,0) and vertices on the y-axis. The minor axis has length 10 and the major…

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Q: 3 sin z If f(2) = then 2 + cos z f'(2) =| f'(5) -

A:

Q: Find the area under the curve y=sin2x from x=0 to x=3pi/4 A. 2 B. 1/2 C. pi D. 3/2…

A: The curve y=sin2x from x=0 to x=3π4

Q: 2. 4. 6. . (2n) n! n = 1 Identify a, 2n! n! 2.4 6 (2n) n! (2n)! n! (2n)! 2 4· 6 • . . · . (2n)…

A:

Q: Evaluate the following integrals? .3 1)S x² e3* dx 2) S dx x²+25 dx 3) 6x – x2 4) | cos(In x) dx

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Find: d/dt (1/square root of 2t) A. square root of 2t/4t B. - 1/square root of 2t C. 1/2t square…

A:

Q: Evaluate the integral (Partial Fraction Decomposition) xdx J (x² + 2)(x² + 1)2

A: ∫xdx(x2+2)(x2+1)2Substitute u=x22→dudx=x→dx=1xdu=12∫1(u+1)(2u+1)2duPerform partial fraction…

Q: Find the area of the region. See Examples 1, 2, 3, and 4. f(x) = (x – 5)3 g(x) = x - 5 y 1.5| 1.0…

A: This question can be solved using the concept of area under curves.

Q: Direction: Find the equation of the tangent lines. Show your solution. 1. f(x)= x2 +5x +1 at (6, -2)…

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Q: Find the value(s) of k that makes the given function continuous. f(z) = { S-3z +4 if r <k -I+3 ifk…

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Q: as well as dll Values Of X where they occur, for the 3' 20X +1 on the domain - 6,5). he derivative…

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Q: e cos xy [ydx + (x + tan xy) dy] = 0 %3D

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Q: The total profit P(x) (in thousands of dollars) from a sale of x thousand units of a new product is…

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Q: IV. On Circular Permutation In how many ways can eight people be seated at a round table? . In how…

A: Note that, in a Circular fashion we can arrange n elements in (n-1)! ways.

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

Q: sin' xcosx dx

A: Indefinite Integration

Q: Question B1 (a) Find the values of a and b such that ax + b – 2 lim

A: Given query is to find the value of a and b.

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Q: eMx cos nx dx

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Q: 1. Find the slope of the line tangent to the graph of the function defined by f(x) = 4 + 2x - x2 at…

A: As you mentioned only 1 solved

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Q: 6. Given i [2, – 5]and i [- 7,2] find %3D а. 5 - b. i C.

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Q: 2/11 Correct Question 4 of 11, Step 1 of 1 2 Consider the function f(x) = x - 6x - 4 on the interval…

A: