Anonymous

# 問幾題微積分

find dx/dy in two ways:

(a)by implicit differentiation.

(b)dy differentiating an explicitformula for y.

1. x^2+y^3=12

2.x+1/y=5

find dx/dy by implicit differentiation.

1.y^2+3xy - 4x^2=9

2.(3x*y^2+1)^4=2x-3y

1.The output of a certain plant is Q=0.06x^2+0.14xy+0.05y^2 units per

day,where "x" is the number of hours of skilled labor used and "y" is the

number of hours of un skilled labor used. currently, 60 hoursof skilled

labor and 300 hours of unskilled labor are used each day. use calculus to

estimate the change in un skilled labor that should be mad to offset a 1-hour

increase in skilled labor so that out put will be maintained at its current level.

2.when the price of a certain commodity is P dollars per unit, customers

demand "x" hundred units of a commodity, where x^2+3px+p^2=79

how fast is the demand x changing with respect to time when the price is

\$5 per unit and is decreasing at the rate of 30 cents per month?

3.A circle oil slick spreads in such a way that its radius is increasing at the rate 20 ft/hr. How fast is the area of the slick changing when the radius

is 200 feet?

4.At a certain factory, output Q is related to inputs "u" and "v" by the

equation Q=3u^2+[(2u+3v)/(u+v)^2] If the current levels of input are

u=10 and v=25, use calculus to estimate the chang in input v that should

be mad to offset a decrease of 0.7 unit in input u so that output will be maintained at its current level.

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