## Practice Problems

Work through the odd-numbered problems 1-19. Once you have completed the problem set, check your answers.

### Problems

1. Fig. 10 shows the tangent line to a function at the point and a line segment units long. On the figure, label the locations of

(a) on the -axis, (b) the point , and

In problem 3, find the equation of the tangent line to the given function at the given point . Use the value to approximate the value of

In problem 7, use the Linear Approximation Process to derive each approximation formula for "close to" .

9. A rectangle has one side on the -axis, one side on the y-axis, and a corner on the graph of (Fig. 13).

(a) Use Linear Approximation of the area formula to estimate the increase in the area of the rectangle if the base grows from 2 to 2.3 inches.

(b) Calculate exactly the increase in the area of the rectangle as the base grows from 2 to 2.3 inches.

11. You are minting gold coins which must have a volume of . If you can manufacture the coins to be exactly high, how much variation can you allow for the radius?

13. Your company is making dice (cubes) and the specifications require that their volume be . How long should each side be and how much variance can a side have in order to meet the specifications?

15. The period , in seconds, for a pendulum to make one complete swing and return to the release point is where is the length of the pendulum in feet and is .

(a) If feet, what is the period of the pendulum?

(b) If second, how long is the pendulum?

(c) Estimate the change in if increases from feet to feet.

(d) The length of a foot pendulum is increasing inches per hour. Is the period getting longer or shorter? How fast is the period changing?

17. For the function in Fig. 14, estimate the value of when

19. Calculate the differentials df of the following functions:

Source: Dale Hoffman, https://s3.amazonaws.com/saylordotorg-resources/wwwresources/site/wp-content/uploads/2012/12/MA005-3.9-Linear-Approximation.pdf

This work is licensed under a Creative Commons Attribution 3.0 License.