1) (a) What is the slope of the line through (−2, 4) and (x, y) for y = x^{2} when:

In general, the slope will be:

i. x = −1.98?

ii. x = −2.03?

iii. x = −2 + h?

(b) What happens to this last slope when h is very small (close to 0)?

(c) Sketch the graph of y = x^{2} for x near −2.

2) The figure below shows the distance of a car from a measuring position located on the edge of a straight road.

(a) What was the average velocity of the car from t = 0 to t = 30 seconds?

(b) What was the average velocity from t = 10 to t = 30 seconds?

3) Use the graph below to determine the limits.

(a) lim f(x)

(b) lim f(x)

4) Evaluate the limit.

5)

6)

7) Use the function h defined by the graph above to determine the following limits.

8) use the IVT to verify each function has a root in the given interval(s). Then use the Bisection Algorithm to narrow the location of that root to an interval of length less than or equal to 0.1.

9) Knowing that , what values of x guarantee that f (x) = x^{2} is within:

(a) 1 unit of 9?

(b) 0.2 units of 9?

10) use the limit definition to prove that the given limit does not exist. (Find a value for e > 0 for which there is no d that satisfies the definition.)

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