Q1: Use Green's theorem to evalute f. (xy + y2)dx + x²dy by the curve y = x and y = x2.

Q: f(x,y) = e (3x² + 3y2)

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Q: Find the points on the curve t² 16t+ 6, y X = = A. a horizontal tangent line B. a vertical tangent…

A: Given the curve is x=t2-16t+6  and y=t2+4t+3

Q: Graph the function f(t) = (/t, 2t +1) by eliminating the parameter.

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Q: Sketch the level curve for f(x, y) = 36 – 9x? – 12y2. '36— 9х2 —

A: Given function f(x,y)=1236-9x2-12y2

Q: 3. Sketch the curve: y = (x²–1)(x+2) x-3

A: y=(x2-1)(x+2)(x-3)y=(x-1)(x+1)(x+2)(x-3)X-intercept:(-2, 0), (-1, 0), (1, 0)Y-intercept:(0, 23)…

Q: Consider the function f(x, y) = 3x²+y²-5 x²-2y A. Find and sketch the domain of f. B. Find and…

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Q: a) Determine the equation of the tangent plane of the graph of the function f(x, y) = 3x²y - 2y³ In…

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Q: Consider the function: f (x,y) = 2x² - 4x - xy² + 2y² - 3. Show and explain that the stationary…

A: The answer provided below has been developed in a clear step by step manner.

Q: Find all points on the graph of x2y − 2x + 63y = 2 where the tangent line is horizontal. (Enter…

A: Differentiate the equation x2y-2x+63y=2 wrt x:  ddxx2y-ddx2x+ddx63y=ddx22xy+x2dydx-2+63dydx=0

Q: Consider the relation between r and y defined by the equation r4/3+y4/3 = 10. Find the r-intercept…

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Q: Find the length (in units) of the curve y =    16 − x2between x = 0 and x = 2.

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Q: Let z = (1+z)√√/50 — x² − y². - (A) Calculate the equation of the tangent plane at x = 3, y = 4. (B)…

A: z = (1 + x)50 - x2 - y2 The given function is of the form z = f(x) To calculate the equation of the…

Q: Let y = f(x) be defined parametrically as y=t+tt, x = 2t -t, te R. Find f(x) and discuss its…

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Q: Assume that y is a function of x. Find (d2y)/(dx2) for x2y-y2-2(sqrt x)+4=0 at point (1,2) 7/6 8/6…

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Q: Let f (x, y) = e(2x-3y). Find the equation for the tangent plane to the graph of f at the point…

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Q: Consider the function z = ƒ(x, y) = 9x3 - 8x2y + 4y3.;Find dz.

A: Consider the given function, z=fx,y=9x3-8x2y+4y3 The formula of the total derivative dz is,…

Q: Determine the equation of the tangent plane of the graph of the function f(x, y) = 3x²y-2y³ In the…

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Q: Find the curve y if dy = x2 +5, dx + 5, curve passes through (0, 25)***

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Q: y = x3 + 2x2 – 5x + 4 of curve x = 2 : Find the equation for its tangent at the apsidal point. |

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Q: Determine the stationary point of the curve y=x-In(1+x).

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Q: Show the curve y(u) = o(u, 1) represents a meridian (line of longitude) on S², while the curve y(v)…

A: Given Information:The curve  and the curve  on .To show:The curve  represents a meridian (line of…

Q: Explain the geometric meaning of r'(t).

A: Let the function is given as ,  rt=ft, gt, ht The derivative of the function is, r't=f't, g't, h't…