Integrate f(x,y) = x+y over the curve C: x² + y²=81 in the first quadrant from (9,0) to (0,9).

Q: dy b) Find the equation of a curve if gradient of the curve at point (x, y) is given by- = 2x3 + x…

A: We have to solve the problem

Q: Find a function f (x, y) that has the line y = 3x - 4 as a level curve.

A: A function is a relation which maps each value in its domain to exactly one value in its range. A…

Q: -2+z) ds over t e point (0, 0, 0)

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Q: F=(x-y², x²•y +3) at A-(1, 1), B=(2, –1) and C=(0,-2). %3D

A: The divergence of a vector field F = <P,Q> is defined as the partial derivative of P with…

Q: Find y in terms of x. dy = x 2 + 5, curve passes through (0, 14) dx x3 A) y = + 5x 3 B y = x3 + 5x +…

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Q: Evaluate fF dR given that F(x, y) = 2yî + (xy – 2x)j and C is the curve in the third quadrant from…

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Q: Evaluate F.dr where F(x, v)=xyi (4, 0).

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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: The slope of the curve 2x + Vx + y = y at the point (0, 1) is

A: 2x + √(x+y) = y  So,  √(x+y) = y - 2x So, x+y = (y-2x)² So, x+y = y² + 4x² - 4xy  So, y(1+4x) - y² =…

Q: Determine the magnitude and direction of the largest change 2 2 (x² + y²)z at the point M (1, -2,1).…

A: Introduction How sharply a curve rises determines its magnitude. It is simplest just examine the…

Q: Find the tangent plane to the equation z = z = 16x + 15y + 19 X - 2x² + 3y² - 3y at the point…

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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: Find ƒxx ( x, y)  and ƒxy( x, y). ƒ(x, y) = 4x2e2y

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Q: The temperature at the point (x, y) on a metal plate is given by T (x, y) = y/(x2 + y2 ). Find the…

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Q: Find the directional derivative of J(, 9) + 3y at the point (2, the direction 57 radians.

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Q: Find the point on the curve y = Vx +1 that is closest to the point (5,0)

A: We will use second derivative test to find the smallest distance among point (5,0) and curve

Q: (4) Calculate faz, fyy, and fry when f(x, y) = 2x4y³.

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Q: Find the gradient of w= 3x² - 5y* + 2z at the point (1, 1, -2)

A: The given function is: w=3x2-5y2+2z2

Q: Find the extrema of f(x,y) = -2x² + y taken on the graph of x + y? = 0.

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Q: From the point (2,2), find the directions in which the directional derivative of f(x,y)=x2 +xy3…

A: Given f(x, y)=x2+xy3 we have to find the directions in which the directional derivative of function…