Find the volume of the solid obtained by rotating the region bounded by the x-axis, the y-axis, the line x = 2, and ye about the y-axis. Round your answer to three decimal places.

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Q: Find all intervals on which the function f(x) = (x² − 3) e-ª is decreasing.

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Q: Evaluate the integral: 16 √ 2² √² + 64 0x = (A) Which trig substitution is correct for this…

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Q: Let g(2) = 42³ +7z7 Determine the most general indefinite integral of g. | (42³ + 7z") dz =

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Q: Choose the correct graph below OA O OB. Oc W NE

A: The derivative of the downward parabola is the line with a negative slope.The derivative of the…

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A: Consider the given table in the question.Given that n = 3&amp;#x25B3;x=b-an"…

Q: M8 ηχη n=1 3"

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Q: 4. Evaluate the integrals. a. b. C. Lou + 3 du +3 6². v³ +3v4 v² √2/43 -dv π/4 3 +7 (cos (0))² (cos…

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Q: Sketch the graph of the piecewise-defined function. Write the domain and range of the function. |x,…

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Q: 16. You are designing a rectangular steel vat with a square base, an open top, and a volume of 32…

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Q: tinues to grow for a while, but then stops growing and begins to decline. The +124t-12312. Find the…

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Q: Find the radius of conv- 00 n! n 1.3.5..... (2n

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Q: Note that: An interior point of the domain of a function f where f' is zero or undefined is a…

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Q: y = In[sin(x + y)]

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Q: Use chain rule to find the derivative of the following functions: a. y = sin(5x) b. y = cos(x²) c. y…

A: We have to find the derivative of the following functions by using the chain rule.Chain Rule: In…

Q: 49. Show that if x > 1, then ln x ≤ x − 1.

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Q: Find the slope of the line tangent to the polar curve at the given point. 7x (-3- r= 6 sin 0; Select…

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Q: 1 7. Ση=0 (2n+1)!

A: The given series is

Q: Let g(t) = - 503 t Determine the most general indefinite integral of g. - 5 + dt

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Q: Given f(x)=x³32, find f'(x)

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Q: was $525, how much mo 10. Nick, an attorney, divided his $15,000 bonus check among three different…

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Q: If g(s) = * · 86 0 g'(s) = √5 + x7 dx, compute g'(s).

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Q: Let h(z) -5+42-42³ 2² Determine the most general indefinite integral of h. I -5+42-423 22 dz P

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Q: Evaluate the limit lim x →0 O -1 1 18 1 9 √81-x-9 X

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Q: 4. n=1 ne-n

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

Q: dr Evaluate the integral: 2² (A) Which trig substitution is correct for this integral? Or=2 sin(0)…

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Q: k. y = ln x 1. m. y = y = 5 cos x + 8 lnx + 3x³ 3x¹+3x²+1 x

A: Given: y= ln(x)Solution: y= ln(x)Differentiating y with respect to x we have dydx= ddx(ln(x)) ⇒y′=1x

Q: Let p(x) be a polynomial of degree 3. Its derivatives, around the point x = -5, are as follows: What…

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Q: 1. Find the derivative of the following functions: a. y = x² b. y=x4 c. y=- X

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Q: Click on the graph to view a larger graph Find the indicated side A || of the triangle ABC given in…

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Q: g. y = tan x h. y = t+√√2t+√1-5t

A: To find the derivative of the following functions.

Q: Find the demand function for the marginal revenue function. Recall that if no items are sold, the…

A: R'(x)= 0.03x2-0.08x+189

Q: For the function f(x)=x^3 - 3x^2 - 9x A. Find the critical points of f(x) B. Where is the function…

A: As per the company's guidelines, we are supposed to answer the first three sub-parts for you, Kindly…

Q: 8. Let f(x) = sinx, g(x) = cos x. The functions f and g, considered on the interval [0, π/2], are…

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Q: Let sin A = -1/sqrt10 with A in QIII and tanB = 3/4 with B in QI. Answer exactly. Find tan (A+B) and…

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Q: Approximate the area under the graph of f(x) and above the x-axis with rectangles, using the…

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Q: 6. Find the equation of the line tangent to the following functions ate the given points. a. y = x²…

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Q: dx f(x) g(x)]-

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Q: Find the area of the shaded region. r = 4 + 3 sin(0) -5 y 5 -5 5 -X i

A: The region is bounded by the curve The given graph of the region