Find the curl of the following vector field: F = (z, 2y, -3x)

Q: P-4 Use separation of variables to find the product solution of the following a) ди ди b) J2u 02u y…

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Q: Compute the area of the region enclosed x² 5x X 1) y 2 2 2 +

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Q: Find the area bounded by the curve y = 4+2x+z² and x-axis from z=-3 to z = -1. Area of the region -

A: y = 4 +2x + x2 A =∫-3-1f(x)dx A = ∫-3-1 4 +2x + x2dx A = [4x +x2 +x3/3]-3-1 A = (-4 +1 -1/3) - (-12…

Q: x+1 2-1 24 - 1 Evaluate the given limit of lim O-1 01/1 0 -¹ O Olimit does not exist if it exists.

A: Solved below...

Q: Suppose that f(4) = 2 and f' (4) = -1. (a) h(x) = (2x². 2x² + 31n (f(x)) h'(4) = (b) h(x) = 20f(x)…

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Q: Find the area of the parallelogram with vertices A(-3, 0), B(-1, 3), C(5, 2), and D(3,-1).

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Q: You are babysitting when the screaming child throws her pacifier out the window. The baby has some…

A: Please see the below picture for detailed solution.

Q: √√√x ²-1 d For the integral What is the re-write of this integral? Ⓒ / - A z² dz 2(z² + 1) B…

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Q: Set up the definite integral required to find the area of the region between the graph of y 19-2 y =…

A: We have to find out area

Q: The graph shows the parabola c(z) = 7-², together with a shaded region. 94 -2 -1 3 + -2 Set up the…

A: The given equation of the parabola is: cx=7-x2 Now find the x-intercept of the given parabola.…

Q: ₁√x³ √4-x² dx. if we let z = √√4-x², which of the following integrals is correct using rationalizing…

A: The given integral,        ∫x34-x2dx

Q: 6) Write an equation of the plane through the points P(5,3,8), Q(6,4,9), and R(3,3,3).

A: The plane passing through the points P5,3,8, Q6,4,9 and R3,3,3

Q: 6) Find dy , where is defined as a function of implicitly by the equation below. dx y + 2x²y³ = 1

A: Given function, y3+2x2y5=1

Q: Determine the amplitude, period, and phase shift for the given function. y = 1 cos 2x - cos(2x - 3)…

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Q: Find area inside 3 - 3 cos 0 and outside r = 3

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Q: The function f(x) = max x, searches for the maximum value between a number. Prove formally that the…

A: Given; f(x)=maxi .xi

Q: 10) Using the First Derivative Test, what are the local extrema for the function 5(x)==x²+10 x³…

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Q: Determine the equation of the ellipse with foci (-8, 14) and (-8, -16), and co- vertices (0, -1) and…

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Q: State what the dot product of two non-zero perpendicular vectors is. Justify your response.

A: We have to find the dot product

Q: 7- Find fx³√3 - 2x² dx

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Q: Determine the equation of the ellipse with foci (1, 4) and (-5, 4), and co-vertices (-2,8) and…

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Q: Q2] Classify the following D.E to: order, degree, homogeneous, and linear: dy 2y=x 3 dx dx

A: We can solve this as follows:

Q: Using the definition of the derivative, find f'(x). Then find f'(-3), f'(0), and f'(4) when the…

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Q: Write TRUE or FALSE before each statement. Solve yy= - dependent variable. Statement 1. The…

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Q: Use the law of cosines to determine the length x in each figure. Leave your answers in terms of…

A: The law of cosine is: c=a2+b2-2abcos C

Q: In APQR, p = 6.7 inches, r = 2 inches and /R=142°. Find all possible values of ZP, to the nearest…

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Q: f cot rda Hint: 1. Final answer should be in terms of cosecant. 2. Any constants that arises due to…

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Q: π I Find the volume of the region bounded above by the surface z = 7 sin x cos y and below by the…

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Q: 7 13 8 a Find the area of the shaded region above.

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

Q: The figure shows the graph of the derivative f' of a function f. Find the critical points of fƒ and…

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Q: need

A: We will solve the problem

Q: The scale of a map measures 1 inch: 1250 miles. If the distance between two cities measures 3 inches…

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Q: 2. Find where the curves intersect, draw a sketch of the region (label it completely), and compute…

A: Region is sketched. And volume is evaluated.

Q: Find the average value of f(t) = -2te Answer: -0.63 on the interval [0, 1].

A: topic- average value of function over interval

Q: Q1: Answer the following matrices: 1 2 3 456 789, . [.. + 3 2 1 654 9 8 7, b)

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Q: The interval of convergence of the following Power Series +∞ Σ nxn 4¹ (n + 1) n=1 ]-4,4] [-4,4]…

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Q: For the given double integral, sketch the region of integration and write an equivalent double…

A: Given problem:-

Q: Set up the definite integral required to find the area of the region between the graph of y= 2²-12…

A: find intersection point

Q: Q3: A. By power series, prove that: d 4 sinhx dx coshx

A: Explanation of the answer is as follows

Q: Find the area of the region between the graphs of y = 16-2² and y=-62 +9 over the interval -3 ≤z≤1.…

A: Given: y=16−x2 and y=−6x+9 Let's first find the intersection point of y=16−x2 and y=−6x+9 16-x2…

Q: Prove that the vectors v= and w= are orthogonal.

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Q: Answer the following. Complete Solution 1. Integrate -2 ex sinx a. dx 0 1+x² 62e

A: F = ∫02exsinx1+x2dxIt is a complex integration hence, numerical method is used.…

Q: Find the length of the arc of a circle of diameter 8 meters sub tended by a central angle 2pi/3…

A: Let "θ" be a central angle in a circle of radius "r". Let "s" be the length of the arc cut off by…

Q: Q1. Evaluate the integral S dx (x + 1)(x² + 1)

A: We need to evaluate the following integral ∫01dxx+1x2+1

Q: Let w=x² +3y² + 2z² where x=rcos, y=rsin 0,z=5t find dw dw ar' at

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Q: 5) Write the equation of the line through the points P(1,3,7) and Q(2,5,11) in: a) Vector form b)…

A: topic - equation of line through two points

Q: Evaluate LL²³ S²x² y² وژ sin z6 dx dy dz

A: To evaluate: ∫01 ∫0z2 ∫03 y2sin⁡z6dxdydz Let, I =∫01 ∫0z2 ∫03 y2sin⁡z6dxdydz First integrate with…

Q: (D² - 6D+9)y = 0

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Q: ∞ The polar curves r = 1 cos and r = 1 + cos are shown in the figure above. Which of the following…

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Q: D is the region enclosed by the parabolas z = y²-9 and 2 - y² +9.

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