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Show all the work... 7. Find the derivative of z = x ln y at the point (1, 2) in

ID: 2839424 • Letter: S

Question

Show all the work...

7. Find the derivative of z = x ln y at the point (1, 2) in the direction making an angle of 30 degree with the positive x-axis. 8. If f(x,y,z) = x^3 + y^3 - z, find the rate of change of f at the point (1,1,2) along the line x-1 / 3 = y-1 / 2 = z-2 / -2 in the direction of decreasing x. 9. Find all relative maxima and minima of f(x, y) = x^3 + y^3 - 3xy. 10. Minimize xy for points on the circle x^2 + y^2 = 1. Evaluate double integral R x dA, where R is the region bounded by y = x and y = x^2. Find the volume of the wedge cut from the elliptical cylinder 9x^2 + 4y^2 = 36 by tgeh planes z = 0 and z = y+3.

Explanation / Answer

Q7) cos(30)= root(3)/2

      sin(30)=1/2

Answer= [cos(30)* partial derivative of Z wrt x] + [sin(30)*partial derivative of Z wrt y]

substitute, x=1 and y=2,    you will get 0.85

Q12) https://alexnegrescu.files.wordpress.com/2013/01/solved-problems-in-multiple-integrals.pdf

check problen 44-23 in the above link