Referring to Figure 11, suppose that F. ds = 37, F. ds = 77 Use Green's Theorem to determine the circulation of F around C1, assuming that curl, (F) = 9 on the shaded region. FIGURE 11 Sc. F - ds =

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A: Since you have asked multiple question, we will solve the first question for you as per our guide…

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A: For critical points ofa function we first find the derivative of the function and equate it to zero.

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A: Given; f(x)=x^2+1/x

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A: We have to answer following Questions.

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A: 0≤x≤10≤y≤xRegion bounded by:x=0, x=1y=0, y=x

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A: Given query is to find the derivative of the expression.

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A: Use moment of inertia concept

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A: Study of integrals in calculus is motivated by calculating the area of a region bounded by curves.

Q: Sketch a single graph of a function f which satisfies all of the following sign charts for f, f',…

A: We need to draw graph.

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Q: Evaluate the function at the given value of x. Round your result to three decimal places. Function…

A: Solve the given

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Q: 2x x– 3)² A = 6, B = 2 A = 2, B = 6 A= 2, B=-6 A=-2, B -6 A= -2,B 6 None of the Above Other:

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Q: Consider the solid of revolution obtained by revolving the region between the curves y=0 and y=x^2…

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Q: Evaluate lim (x)/

A: We can find the  limit as below.

Q: Write the expression as a single Integral -3 1. Sf f(x)dx + S, f(x)dx = -3 - 3. S f(x)dx + S, f(x)dx…

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Q: H.W (5) Solve the following differential equations of (x'+y')dx+(2xy cos y)dy phee

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Q: Find the derivatives of the following functions: Inx i) y = sin3x? ii) y = e2*cosx iii) y = 3r+5

A: i)y= sin 3x2y' =ddx sin 3x2y' =cos 3x2  ddx(3x2)y'=cos 3x2 (3)(2x2-1)y'=(6x) cos 3x2

Q: mparison test to determine whether the given series conve:

A: Please refer to the image below

Q: 2r³ – 4x² – x – 3 dr x² – 2x – 3

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Q: Solve for x in the following expression using the quadratic formula. 3x2 + 19x – 4.9 = 0 Use at…

A: We can solve this as follows:

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A:

Q: Verify that the Intermediate Value Theorem applies to the indicated interval and find the value of c…

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Q: Find the angle between the vectors (8, 6) and (-9, 7). Carry your intermediate computations to at…

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Q: 3 + In?x dx

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Q: Find V · (F × G), if F(x,y, z) = 3xi+j+7yk and G(x, y, z) = xi+ yj – zk. V• (F × G) =

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Q: Q1: Find partial derivatives of the function with respect with each variable 3) f(x, y) = (xy – 1)}…

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Q: nd the S (1–) dx A. x– 2 In|x| – +c B. 3x – 2 In|x| –-÷+c C. 2x – In|x| –+c D. x– In|x| - +c

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: If f(x) = cos(2x) then find II f (t|4)

A: Given query is to find the Indicated derivative.

Q: Evaluate the double integral over the rectangular region { 2(* sin(1) – y sin(z) dA; R= {(x,v) : 0 <…

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Q: In(1+x) -x cosx -1 1. lim x-+0 7- In(2x + 3) 3. lim x-00 In(5x -2)

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Find the average value of the function f(x,y)=eˆ(y/x) over the region bounded by y=x, the x-axis and…

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Q: Determine the value of t that maximizes the area above the x-axis and below the graph of the…

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Q: Find the divergence of the vector field F. F(x, y) = 5x2i + 5y²j

A: The given vector field is: F(x,y)=5x2i+5y2j Let, F(x,y)=F1i+F2j⇒F1=5x2, F2=5y2

Q: Find all refative extrema and saddle points of the function. Use the Second Partials Te f(x, y) = x…

A: Here,  we have given a two variable function and we have to find out all the relative maxima and…

Q: Find f. (a) f'(x) = 3x4 – 5x? + x

A: Given query is to find the function.

Q: Verify Green's Theorem by evaluating both integrals | y2 dx + x2 dy dA ду for the given path. C:…

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Q: Find the volume of the region enclosed by z = 1 – y? and z = y² – 1 for 0 < x < 21. V =

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Q: Find the volume of the solid formed by rotating the region enclosed by x = 0, x = 1, y 0, y= 4+ x°…

A: Here we have to find the volume.

Q: 1 :? 5+ x² Which of the following is an antiderivative of the function f(x) : %3D (a) 2x In(5 + x²)…

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