Evaluate [F·dr if F(x, y)=(x²y)ī +(xy²)ƒ and the curve C is given by r(t) = (t²)i + (t)j, 0≤t≤1.

Q: 2. Find y in terms of x if = 6x² – 2x and the curve passes through the point (1, 5). -

A: We have to find the value of x if dydx=6x2-2x and the curve passes through the point (1,5).…

Q: a. Find a function (f(x,y,z)) such that (F = Vf(x,y,z))? b. Use part (a) to evaluate (F. dr ) along…

A: We have to evaluate the ∫CF.→dr→.

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: What curve is described by the function (t) = (2t + 3) + i(t - 5), 0 ≤ t ≤ 1

A: Step:-1 Given parametric function is ft =2t +3 +i t-5,  0≤t≤1 Here,  x=2t +3  ---(1)y=t-5  ---(2)…

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: Let P = (x,y) be a point on the graph of y = x- 12. %3! Express the distance, d, from P to the…

A: The given problem is to find the distance function in terms of x where distance between origin and…

Q: Consider the point (x,y) lying on the graph of the line 8x + 7y = 3. Let L be the distance from the…

A: We use the distance formula

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) = e3x-49). 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: Let P= (x,y) be a point on the graph of y = x. Express the distance, d, from P to (7,0) as a…

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Q: Let f (x, y) = e(5x-6y). Find the equation for the tangent plane to the graph of f at the point…

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Q: Let f (x) = vx² – 2x + 2 + Vx² – 6x + 13. Find the point(s) on the graph of f at which the tangent…

A: See the handwritten solution