Given that 3 L³ex ex dx = e³ - e, use this result to evaluate [²³3 3ex + 2 dx.

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Q: 8. Rewrite CLI x+2 dydadz in the order dzdxdy.

A: We need to change the order of integral.

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Q: Evaluate x dS, where S is the part of S the plane 2x+y+z=4 in the first octant.

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Q: Use a Riemann sum to approximate the area under the graph of f(x)=x² on the interval -2≤x≤2 using n=…

A: The midpoint rule∫abf(x)dx≈Δx(f(x0+x12)+f(x1+x22)+⋯+f(xn−2+xn−12)+f(xn−1+xn2))Δx=b−an

Q: What is the lim f(x) for the following graph? X-3 ㅇㅇ 01 6 3 5 4 3 2 1 0 -1 O-2 -2 리 스 -5 -4 -3 -2 -1…

A: A graph of the function is given.The aim is to find the limit .

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Q: valued Func r(t) = - + 3 + 5tk O -2 -2 y 5 2 2 Find its length over the given interval. √32 [0, 1]…

A: r(t)=-ti+3tj+5tk ,[0,1]

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A: A graph of the function  is given.The aim is to sketch the graph of the derivative function.

Q: b(x) = √√√x Answer O 21 2√2|x| t(x) = 2x

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Q: Calculate af ax af Əy = af af af af ax' ay ax (1,-1) ду f(x, y) = e0.9xy = ax (1,-1) af ay (1,-1)…

A: f(x,y)=e0.9xy

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Q: a) dy dx dy b) = dx dy dx c) = x² + e10x = yx³ In(x) ey

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Q: Show that the function f(x) = x4 + 8x + 6 has exactly one zero in the interval [-1, 0]. ... Which…

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Q: Find inflection point(s) for f(x), if any. f(x) = 27x - x³ A. f(x) has an inflection point at x = -3…

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Q: Express the following statement using absolute value notation: In an experiment, the measurement of…

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Q: 29. a(t) = -32; v(0) = 70; s(0) = 10 30. a(t) = -32; v(0) = 50; s(0) = 0 31. a(t) = -9.8; v(0)=20;…

A: 29) a(t)=-32, v(0)=70, s(0)=1031) a(t)=-9.8, v(0)=20, s(0)=0

Q: 10. x³ .3 = 2x-y x+3y

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

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A: The objective of this question is to find two numbers whose sum is 9 and whose product is a maximum.…

Q: The parametric equations and parameter intervals for the motion of a particle in the xy-plane are…

A: x=4cos⁡(2t),y=4sin⁡(2t),0≤t≤π

Q: 31. Assume that f is continuous and 2x S f ₁ f(t) d² = 4 + x²" dt (a) Determine f(0). (b) Find the…

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Q: Question The graph of f(x) is given below. Select each true statement about the continuity of f (x)…

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Q: Determine the resulting definite integral after making the following substitution: • ¹/3 So 1 4+9x²…

A: I =∫01/314+9x2 dx

Q: Question Given the graph of f(x) below, Identify the graph of f'(x). Select the correct answer…

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Q: 1 A 3 2 1 a 1 To find the blue shaded area above, we would calcula b f(x) dx = area Where: a = 1…

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

Q: 32. Assume that f is continuous and S f(t)dt = sinx -x cos.x. (a) Determine f(π). (b) Find f'(x).

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Q: A cell culture contains 4 thousand cells, and is growing at a rate of r(t) thousand cells per hour.…

A: Substitute t=5 in r(t) and solve, an then add 4 thousand to it.

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A: To evaluate the following definite integral.

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A: The given integral is Sin(7x2), limit from 0 to 0.76.

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Q: (Technology Permitted) Find the area of the region enclosed by the graphs of f(x) = - 3x +6 and g(x)…

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Q: If the birth rate of a population is b(t) = 2300e0.022t people per year and the death rate is…

A: The given data is:To find the area between these curves for

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Q: Find the mass of a wire that lies along the curve r(t) = (t² −8) j+2tk, 0≤t≤2, if the 3 density is…

A: As per Bartleby guidelines for more than one question asked only one is to be answered please upload…