Question 1 part A

Find dz for z=3x²-5xy³

a. (6x-5)dx-15xy²dy

b. 6x dx-5y³dy

c. (6x-5y³)dx-15xy²dy

d. (6x-5)dx-5y³dy

Question 1 part B

For the given function evaluate dz if x = 2, y = 0, dx = 0.1, dy = 0.2.

z = x³e^2y

^{a. 2.4}

^{b. 4.0}

^{c. 4.4}

^{d. 1.6}

Question 1 part C

FInd dw for w = x²lny + yz

a. 2x lny dx + z dy + y dz

b.2x dx + [(1/y) + 1] dy + dz

c.2x lny dx + [(x²/y) + z)] dy + y dz

d.(2x/y) dx + dy

Question 1 part D

Use the total differential to approximate 3.97 e^0.02

^{a. 5.1}

^{b. 4.05}

^{c. 3.96}

^{d. 3.99}

Question 1 part E

The manufacturing cost of an appliance is given by M(x,y) = 15x²+10y²-12xy+100 where x is the cost of parts and y is the cost of labor. The company currently spends $20 on parts and $15 on labor. Use differentials to approximate the change in cost if the company begins spending $20.25 on parts and $$15.50 on labor.

a. 225

b. 135

c. 150

d. 300