Find the area of the region. See Examples 1, 2, 3, and 4. f(x) = -x + 7 6. g(x) = = y 81 6 2 bo 2.

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Q: what

A: Please refer to the image below

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A: density=massvolume For  density to become maximum, volume needs to be minimum. Given

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A: Since you have posted multiple questions which are not interlinked i can do first question as per…

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A: Given problem:- ∫ 3t3(t2+4)5 dt

Q: Solve using trigo substitution

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Q: 8. S 3tan 3z r sec? 32 da

A: As per the guidelines I can solve only first question

Q: FIND THE GIVEN DIFFERENTIAL EQUATION Homogeneous Equation (x + y - 3) dx + C x -y + 1) dy • 0

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Q: SIXE-A Consider the graph shown to the right 4. lim f(x) X-axis 5. Evaluate lim f(x) X+3" 6. lim…

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A: This is a problem related to vector. Based on the general formula and concept we will answer the…

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Q: Give the generator, the directrix, and the rulings of the cylinder x = lnz. Draw a sketch of the…

A: We need to give generator, the directrix, and the rulings of the cylinder x = lnz.

Q: Is 3 A m, m being any real number, possible? Explain. [IC]

A: This is a problem related to vector parts. Based on the general formula and concepts we will answer…

Q: where did you get 10 and 6?

A: Here we have assumed that each rectangular run is x feet by y feet. That means: length = x width = y…

Q: 6y² -dA where D is the region in the 1st quadrant bounded by y =x' and y= 4x . Evaluate 9.

A: Here we have to evaluate the  integral of a function over a region.

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Q: Find the 44th derivative of the function f(x) cos(2). = The answer is function f 144) (æ) = cos (x)…

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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 GIVEN DIFFERENTIAL EQUATION Exact Equation ( 2% ty cos x) dx + sın x dy = dy = 0

A: The given differential equation,      2x+y cosxdx+sinx dy=0

Q: f(x) f'lx) %3D

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Q: 12. Given f (x) = x³ – 12x + 1 (a) Find the intervals on which f(x) is increasing or decreasing. (b)…

A: I have appended the formula used in the solution part.

Q: 19. Using the l'Hospital's rule to find the limits e3r – 1 In(ln æ) 1 e" – 1- x – ² (a) lim a→0 In(x…

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Q: .4 dx (x² + 9)2

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

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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: A problem or equation of the tangent line to a curve at the point (1,3) is y = x+2. If at any point…

A: Let's find.

Q: Evaluate the following limits if they exicts, show complete solution.

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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…

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Q: 9. Find the volume of the parallelepiped defined by the vectors. [8, – 3,4] [- 2,9, 1] w = [0, – 4,…

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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 area of the region enclosed by y = 5x and x = 6.5 - y. 2- 3 4 5 6 Use horizontal strips to…

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Q: —x2 — 4х + 18 (Зх+ 4) (x? + 9)"*

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Q: 18 of 19 50 where T<0< 4r as shown in the diagram A rubber ball is being spun in a outward spiral in…

A: Let's find.

Q: What is the equation of the line that contains the vertices of the hyperbola (z+ 4)2 (y+2)² = -1? 16…

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

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Q: Find 4 [3f (x) – g(x)]dx = i if 4 4 |r)dx = 4 and g(x)dx = 20

A: This question is related to definite integration, we will solve it using given information.

Q: Evaluate the integral (2x + 6)dx x² – 2x + 17

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