# Practice Problems

## Problems

1. What is the slope of the line through and for and ? ? ? What happens to this last slope when is very small (close to 0)? Sketch the graph of for near .

3. What is the slope of the line through and for and ? ? ? What happens to this last slope when is very small? Sketch the graph of for near .

5. Fig. 9 shows the temperature during a day in Ames.

(a) What was the average change in temperature from 9 am to 1 pm?

(b)
Estimate how fast the temperature was rising **at **10 am and **at **7 pm?

(a) What was the average velocity of the car from to seconds?

(b) What was the average velocity from to seconds?

(c) About how fast was the car traveling at seconds? at at ?

Problem 9 defines new functions in terms of AREAS bounded by the functions and . This may seem a strange way to define a functions , but this idea will become important later in calculus. We are just getting an early start here.

9. Define to be the area bounded by the and y axes, the horizontal line , and the vertical line at (Fig. 13). For example, is the area of the 4 by 3 rectangle.

a) Evaluate and .b) What area would represent in the figure?

c) Graph for .

Source: Dale Hoffman, https://s3.amazonaws.com/saylordotorg-resources/wwwresources/site/wp-content/uploads/2012/12/MA005-2.1-Tangent-Lines-Velocities-Growth.pdf

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