Math

MA 141 Turn in Homework 3.7

SHOW YOUR CALCULUS! Pitts Name ______________________

1. (#12) Find the differential of the function 2

2 1 ( )

1

x f x

x

 

 . Simplify!

2. (#22) Use differentials to approximate the 99.7 . Use your calculator to find the exact value and

compare the two.

Estimate using differentials. Actual value (rounded to 3 decimal places)

3. (#32)The volume of a spherical cancerous tumor is given by 34

( ) 3

V r r . If the radius of a tumor is

estimated at 1.1 cm, with a maximum error in measurement of 0.005 cm, determine the error that might

occur when the volume of the tumor is calculated using differentials. Show your calculus.

4. (#36) The relationship between Cunningham Realty’s quarterly profits, P(x), and the amount of money x

spent on advertising per quarter is described by the function: 21

( ) 7 30 (0 50) 8

P x x x x      .

Where both P(x) and x are both measured in thousands of dollars. Use differentials to estimate the

increase in profits when advertising expenditure each quarter is increased from $24,000 to $26,000.

5. (#38) The supply equation for a certain brand of radio is given by ( ) 0.3 10p s x x   where x is the

quantity supplied and p is the unit price in dollars. Use differentials to approximate the change in price

when the quantity supplied is increased from 10,000 units to 10,500 units.

6. (#42) A certain country’s government economists have determined that the demand equation for

soybeans in that country is given by 2

55 ( )

2 1 p f x

x  

 where p is expressed in dollar/bushel and x, the

quantity demanded each year, is measured in billions of bushels. The economists are forecasting a

harvest of 1.8 billion bushels for the year, with a maximum error of 15% in their forecast. Determine

the corresponding maximum error in the predicted price per bushel of soybeans using differentials.