Partial Derivative 1.) Find the plane point on the 4x 2y + z = 1 plane that has the closest distance to (−2, 1, 5)

Q: Caleulate all first ordeT partial derivatives of the finction y 2nin(r²) ekan '(-y) + + cos2(xz2)

A: We need to calculate all first-order partial derivatives of the function w=yz…

Q: difference between the relative errors in x and y. Given that u = 5.xy2 , &r, E, and & denote the…

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Q: Calculate directional derivatives and gradients in three dimensions. Find an equation for the…

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Q: Find an equation of the tangent plane to the surface at the given point. 4x2 + 2y? + 4z2 22, P = (2,…

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Q: B) Determine the volume of the solid obtained by rotating the region bounded by : y=x -2x and y= x…

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Q: f(x, y) = x² - y² + 10x +12y - 64 −x² −

A: To determine the extrema if any for the given function.fx, y=-x2-y2+10x+12y-64

Q: What are three majors applications of partial derivatives? This question has multiple answers.…

A: To find:  thee major applications of partial derivatives from the given options.   since partial…

Q: Solve for an equation of tangent plane and parametric and symmetric equations of normal line to the…

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Q: |(x+y*) sin- 1 (х,у) # (0,0) f(x, y) = X + y? (х, у) 3 (0,0) fx (X, y) fy(x.y) (0,0) Find out if the…

A: Ww will use the definition

Q: Find the four second partial derivatives. Observe that the second mixed partials are equal. z =…

A: Given:      z=22xey-11ye-x      ∂z∂x=∂∂x22xey-11ye-x               =22ey∂∂xx-11y∂∂xe-x…

Q: f(x, y) = = /25 - (x - 2)² - y²

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Q: Find the equation of the tangent line to the curve of intersection of the surface z = x² - y² with…

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Q: 9(2, u, 2) sin(y) gx, y, z

A: The given function is: g(x,y,z)=x sin(y)z2

Q: 10 Draw the graph of f and its tangent plane at the given point. (Use your computer algebra system…

A: Consider the function. Graph the surface and the tangent plane at the given point. To sketch the…

Q: Tangent drawn from the point (4, –3,10) to the intersection curve of z = x² and z = 25 – y² surfaces…

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Q: Find the four second partial derivatives. Observe that the second mixed partials are equal. z =…

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Q: Find an equation of the tangent plane to the surface at the given point. 6x² + 2y² + 4z² = 30, P=…

A: NOTE: Refresh your page if you can't see any equations. . the function f is

Q: Consider the surface z = sin(ry). (a) Use the Second Partial Derivative Test to find any critical…

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Q: Region bounded by: y = x+1, y = -x + 4, x = 0 Rotate about: y-axis %3D

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Q: Find the four second partial derivatives. Observe that the second mixed partials are equal. Z = 19xe…

A: Given, z=19 xey-9 ye-x

Q: What are three majors applications of partial derivatives? This question has multiple answers.…

A: There are many applications of partial derivatives like to find Maxima, minima, saddled point,…

Q: Find the four second partial derivatives. Observe that the second mixed partials are equal. z =…

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Q: The equation of a surface is given as (x.y) = e"(x² -xy + y*). (i) Calculate all first and second…

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Q: 5. (10 points) Find an equation of the tangent plane to the surface given by z2 – 2x2 – 2y² = 12 at…

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Q: Find the four second partial derivatives. Observe that the second mixed partials are equa z = 5xe-…

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Q: Use partial derivatives to find the coordinates which give the shortest distance from the point…

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Q: Find the tangent plane to the equation z = 3x? – – 60) - y² – 4y at the point (4, 2, - -

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Q: Find the four second partial derivatives. Observe that the second mixed partials are equal.…

A: The given function is hx,y=xx+y.

Q: 1. Find the volume generated by revolving about the line y = 0 the area under the arch of the sine…

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Q: Evaluate fy and fy at the given point. f(x, y) = arctan(2), (5, -5) Part 1 of 4 Consider y to be the…

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Q: Compute the first-order partial derivatives. z = 5y* (Express numbers in exact form. Use symbolic…

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Q: Find the four second partial derivatives. Observe that the second mixed partials are equal. z =…

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Q: Explain how a directional derivative is formed from the two partial derivatives f, and f,. Choose…

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Q: volume of the solid generated by the curve e-", between x = 3 and x = 8 about the axis is

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Q: 9-x²-y² is the upper √y half of the disc centered at origin with radius r = 3 The domain of f(x, y):…

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Q: y = Volume = s 1 x4' y = 0, x = 3, about the line y = -3 using the method of disks or washers. and x…

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Q: The gas law for a fixed mass m of an ideal gas at absolute temperature T, pressure P, and volume V…

A: First of all, consider the given equation.Divide both sides of the equation by V to get the equation…

Q: Stokes' theorem is given by curlF = SP which is a generalization of Green's theorem. i) State TWO…

A: i) To state two dissimilarities between Green's and Stokes' theorem.

Q: Find the center of mass of a thin plate of constant density & covering the given region. The region…

A: Let's find center of mass.

Q: Explain why the function is differentiable at the given point f(x, y) - y + sin (0, 8) The partial…

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Q: Region Ris enclosed by the curve y = 2 Vx – 3, the line y = 4, and the line a = 3. y = 2/z – 3 y = 4…

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Q: container is formed by revolving the region bounded by the graph of  y = x2 , and the x-axis, 0≤ x…

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Q: The region bounded by the curve y=x²-2 and the lines y=-2 and x=2 is rotated about the line y=-2.…

A: The two curves are y=x2-2  &  y=-2 & x=-2

Q: Find the extreme values of the function f (x,y) = 2 - 4x - - y² on the closed region bounded by the…

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Q: Find an equation for the tangent plane to the surface z + 4 = ry* cos(z) at the point (4, 1, 0)

A: Solution: The objective is to find an equation for the tangent plane to the given surface

Q: Find the center of mass of a thin plate of constant density ô covering the given region. The region…

A: Given :-  The region bounded by the parabola x = 4y2 - 2y and the line x = 2y. To Determine :-  The…

Q: Find the minimum distance from the surface x2 -y2 -z2= 1 to the origin.

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Q: 8. Find the centroid of the first quadrant area bounded by x2 + y – 4 = 0

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