The value of(2xy x²) dx + (x+y2)dy, where C is the enclosed curve of the region1by y=x² and y2=x, will be given by:07boundec Question 17The gradient of the functionOA (OT-P-¹)f(x,y,z)=ye-x²²sin (yz.) at point (-1, 1, ) is given by

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Answered: $(2xy - x²) dx + (x+y²)dy, where C is…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter7: Integration

Section7.1: Antiderivatives

Problem 2E

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flx.y)=X P=(-3,;4h V=2-23 A. Find the gradient of f. Vf = 1/y i+ -x/y^2 Note: Your answers should be expressions of x and y; e.g. "3x - 4y" B. Find the gradient of f at the point P. (Vf) (P) -1/4 i+ 3/16 Note: Your answers should be numbers C. Find the directional derivative of f at P in the direction of v. Duf = (-7sqrt2)/32 Note: Your answer should be a number D. Find the maximum rate of change of f at P. 5/16 Note: Your answer should be a number E. Find the (unit) direction vector in which the maximum rate of change occurs at P. i+ Note: Your answers should be numbers
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f(x,y) = x2-y2 There's a two-dimensional line that goes through the point (5,4) and is parallel to the gradient of (5,4). What's the slope of that line? How does it compare to (dy/dx) at (5,4)? Thanks.
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f(x,y) = x2-y2 What's the slope of the two-dimensional line that goes through (5,4) and is parallel to the gradient of (5,4)? How does this differ from (dy/dx) at (5,4)?

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$(2xy - x²) dx + (x+y²)dy, where C is the enclosed curve of the region boundec. The value of by y=x² and y2=x, will be given by: 20 7