Let f(x, y) = axy + ax²y + y³. (a) div(grad(f)) : = (b) Find a so that div(grad(ƒ)) = 0 for all x, y. a =

Q: MATH CALCULUS Solve the system or show it has no solution. If there are infinite numbers of…

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A: Graph is given . We have to find the domain and Range .

Q: • [F(x) dx (a) Given f(x) dx = 7 and (b) (c) (d) [²² [[9 L²90 [f(x) + g(x)] dx [²² [g(x) = f(x)] dx…

A: ∫29f(x)dx=7∫29g(x)dx=-3rule:∫abcf(x)dx=c∫abf(x)dx  , where c…

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Q: {(1, 2), (2, 5), (3, 7), (1,3)} {(3, 3), (4, 5), (5, 11), (6, 13)] 9. 10.

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A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: 2. Please, provide a real world example for each type of sequence arithmetic and geometric.

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Q: 6. What is the equation for the slope of the ellipse+-1 at 1 at (x₁, ₁)? A. B. C. D. E. y' = -21 y'=…

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Q: F(W) = + [TS(W-5) + 3 (W-5) +TS(W+5) + = 1/2 [717 S(W_S) + TS(W+S) + = [TT-S (W-S) + -S(W-5) + πTS…

A: The term in the circle is wrong. I have showed the correct term which should come after simplifying.

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Q: Let F = (1yz)i + (5xz)j + (1xy) k. Compute the following: A. div F = B. curl F = C. div curl F i+ j+…

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Q: +8 (x² − x + 1)(x² + 9)²

A: The objective of the question is Write out the form of the partial fraction decomposition of the…

Q: 36. f(x) - 8 x-2x²x2 If lim = 3, find lim f(x) x-2

A: As per our company guidelines, we are supposed to answer only the first question, please repost…

Q: 26. What does the alternating series test tell us about A. The series is converges absolutely. B.…

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Q: Compute the average rate of change of the given function over the specified interval. f(x)=x^3,[6,7]

A: Given query is to find average rate of change for the interval [6,7].

Q: A graphing calculator is recommended. Straight-line depreciation is a method for estimating the…

A: Given formula:- Value=Price -Price-scrap valueUseful Lifetime t, For 0≤t≤Useful lifetime

Q: 9-30. Finding area Determine the area of the shaded region in the following figures. V X y=x²-2

A: We have given to find area of shaded region  Region is bounded by two curves  y=x ........(i) y=x2-2…

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Q: AERCISES 3.4 Express each equation of the ellipse in standard form. Then give the coordinates of the…

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Q: A graphing calculator is recommended. For the function, consider the following. nd g(--/-) g(x) =…

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Q: Write the equation of the circle centered at ( – 9,5) that passes through ( – 17, 16).

A: We have to find the equation of circle.

Q: B) Find the limits (don't use L'Hopital's rule): sin(sin h) sin h 1) lim h-0 √√√1+x-1 x 2) lim- x-0

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A: Given curve, y=-x321,-26≤x≤0

Q: 2. {(-2,4), (-3,4), (-4,4)} 3. f(x) = 4x + 5 4. N 2 y=5

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Q: Given the graph of f(x) shown, answer the following. f(x) 4 (a) What is f-1(−1)? -2 15 10 5 5 10 -15…

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Q: If f(x) = 47 +5√x + 13 and g(x) = 2x² + 5, compute the composition (fog)(3). (fog)(3) =

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Q: Solve for x using the system of 6. equations. 7y = 5x and 35 + 4x = 3y

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Q: (5x)” Σ 14" n=1 (Use symbolic notation and fractions where needed. Give your answers as intervals in…

A: Since multiple questions are asked, I am answering first question.

Q: Express (5x + 7y, 8x + 5y, 0) as the sum of a curl free vector field and a divergence free vector…

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Q: 44. Given the alternating series: 1-+-+632... What is the error bound for an 80 term calculation? A.…

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Q: 2 ГБА 0 4 - x - y dy dx

A: ∫01 ∫024-x-y dydx

Q: 'm sorry the point is -3/2 (negative three halves) not -32

A: The Solution is given below-

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A: Given; Radius=9 feet Arc length=5 feet

Q: -1 y 6 5 4 3 2 1 -1 -2 -3 (2,5) b 1 2 (2,-2) 3 4 5 5 a 6 6 7 8 9 (8,-2) x

A: As we know that; The  expression for the distance between two points Px1,y1 &amp; Qx2,y2 is:…

Q: Find the average rate of change of the function from x=1 to x=4 of f(x)=-8/x^2

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Q: 3. The 3rd term of a geometric sequence is 12 and the 7th term is 192. Determine the 13th term.

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Q: The conversion of temperature units from degrees Fahrenheit to degrees Celsius is given by the…

A: Given query is to find composite function.

Q: For the pair of functions f(x) and g(x), find f(g(x)), g(f(x)), and f(f(x)). f(x) = x³; g(x) = 4x -…

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Q: C] Write in interval notation -3 -2 -1 0 1 2 3 4 -1 0 1 2 3

A: We can write the answers in the following steps.

Q: Question 29 4π Find the area of the sector of a circle with radius 6 centimeters formed by a central…

A: Topic- Area of Sector

Q: Find an equation of the tangent to the curve at the given point. x = sin(?t),      y = t2 + t;…

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Q: Q1: A-Show if the series is convergent or divergent (2n)! n!n" n=1

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

Q: In the given equation, find dy/dx by implicit differentiation. O (3x²+tan-ly)(1+y²) (1+y)e-x O…

A: Basic identities of differentiation is used.

Q: Q6A A-Graph the cubic shape formed by connecting the eight points {(0,0,0),(0,1,0),(2,0,0),…

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Q: EXAMPLE 6 Using the second-derivative test Use the second-derivative test to determine whether each…

A: Given Equation: f(x)=3x5-5x3+2