Reference no: EM13918569

1. (i) What is the slope of the line through (-1, -2)and (x,y) for y = x2 + x - 2 when:

a) x = -0.98?

b) x = -1.03?

c) x = -1 + h?

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

(iii) Sketch the graph of y = x2 + x - 2 for x near -1.

2. Use the graph below to determine the limits:

(i) lim f(x) x→1
(ii) lim f(x) x→2
(iii) lim f(x) x→3
(iv) lim f(x) x→4

3. Evaluate each limit:

(i) lim??→1 ??2+3??+3 ??-2
(ii) lim??→-1 sin?(??)??
(iii) lim??→9 √??-3 ??-9

4. Use the graph shown below to determine the limits:

(i) lim??→2h(5 - ??)

(i) lim??→0[h( 3 + ??) - h(3)]

5. Describe the behavior at each integer of the function y = f (x) in the figure provided ,using one of these phrases:

• "connected and smooth"
• "connected with a corner"
• "not connected because of a simple hole that could be plugged by adding or moving one point"
• "not connected because of a vertical jump that could not be plugged by moving one point"

6. At which points is the function in the graph below discontinuous?

7. If you apply the Bisection Algorithm to the function graphed below, which root does the algorithm find if you use:

(i) starting points 0 and 9?
(ii) starting points 1 and 5?
(iii) starting points 3 and 5?

8. Use the function f defined by the graph below to determine the following limits:

(i) lim ??→2+ ??(??)
(ii) lim ??→2- ??(??)
(iii) lim ??→2 ??(??)
(iv) lim ??→1+ ??(??)
(v) lim ??→1- ??(??)
(vi) lim ??→1 ??(??)

9. You have been asked to cut two boards (exactly the same length after the cut) and place them end to end. If the combined length must be within 0.06 inches of 30 inches, then each board must be within how many inches of 15?

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

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

(ii) About how fast was the car traveling at t = 10 seconds?

(iii) What does the horizontal part of the graph between t = 15 and t = 20 seconds tell you?

(iv) What does the negative velocity at t = 25 represent?