Find the area of the shaded region. -1.0 -0.5 y 8 6 y=3e 4 2 0.5 (1, 3e) y=3xet² 1.0 1.5 2.0 X +

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

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A: To find the critical numbers of the following function.

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A: {y|y = x2 − 3, x  integers}

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A: The given equation  is

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A: x=tcos⁡(t),y=t−6sin⁡(t),

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A: The Product Rule:The Quotient Rule:

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A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

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A: The given function .The aim is to find all values of  and  such that .

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Q: What values of a and b make the function f continuous everywhere? x² 4 a = f(x) = and b = - " X 2…

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Q: Let h(v) = 4v v² +6

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Q: (3) Redo Question (2) of Homework 1 using the Exact approach 2xydx + x²dy = 0

A: Given Differential Equation is as follows

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A: g(t)=sin⁡(ln⁡t)

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A: To determine whether the sequence  converge or diverge.To find the limit if the sequence is…

Q: Give the partial fraction decomposition for the following expression. x² - 6x +29 2 X (x - 5)(x-1)(x…

A: we need to give partial fraction of

Q: Evaluate the indefinite integral. 0+ +C 54 sin x COS X dx

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Q: Calculate the derivative of y with respect to x, if x³/² + y-5/2 = 7. dy dx

A: Given equation, .derivative rules:

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A: L=limx→∞xe−x/2

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Q: Suppose the solid W in the figure is one- quarter of a circular cylinder of height 4 and radius 6…

A: Suppose the solid W in the figure is a one quarter of a circular cylinder with a height 4 and radius…

Q: Find the exact length of the curve. x = et t₁ y = 4et/2, 0≤t≤4

A: Given, .Formula for length of curve is,

Q: conditions

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Q: f has ---Select--- 2 (Order your answers so the x-coordinates are in order from least to greatest.)…

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Q: Find the absolute maximum and minimum values of the function over the indicated interval, and…

A: The function is given byTo determine: The absolute maximum and minimum values of the function.The…

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Q: Help determine the difference quotient and for f(x)=x^2+4

A: Given,. Difference quotient=

Q: 7. 8. 9. sect cos t sect 1+sec²x tan*x+1 sin t csc t = sin t = cos x + 1 cos t sect = 1

A: Given.

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Q: Evaluate the following integral using trigonometric substitution. x² √√64-x² S dx

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Q: Evaluate the indefinite integral. Answer = +C St tan¹ (2x) dx

A: Let,  A=.

Q: The edge of a cube was found to be 30 cm with a possible error in measurement of 0.4 cm. Use…

A: The edge of a cube was found to be 15 cm with a possible error in measurement of 0.1 cm.By using…