M120 Project #1

Date due: 25 points

Objective: Ownership of the concept of limit *5 pt penalty for each class day late

Description

1. Produce a table showing a sequence of x-values and the corresponding f(x) values.

2. Each function below should be evaluated at no fewer than 5 x-values each side of the stated x-value if the x value is finite and no fewer than 8 x-values when the stated

x-value is . See examples below. Use x-values of -2, 0, and for each function, i.e. 3 tables per problem.

3. Use the results of the table above to determine if the function value is approaching a specific limit. If it is, state that value. If not, state that no limit exists. A limit of is possible. Again, see the examples below.

1. 2.

3. 4.

5. 6.

Examples

1.

x	-2.5	-2.2	-2.1	-2.01	-2.0003	-1.9998	-1.99	-1.9	-1.7	-1.5
f(x)	11.25	9.84	9.41	9.0401	9.0012	8.9992	8.9601	8.61	7.89	7.25

Conclusion As x approaches -2, f(x) approaches 9; i.e.

2.

x	-1.0	-0.5	-0.1	-0.01	-0.0003	0.0002	0.001	0.1	0.5	1.0
f(x)	-1	-2	-10	-100	-3333	5000	1000	10	2	1

Conclusion As x approaches 0, f(x) does not approach any particular value;

i.e.

3.

x	10	200	500	1750	40,000	525,000	900,000	1,200,000
f(x)	.1	.005	.002	.00057	.000025	.0000019	.0000013	.00000083

Conclusion As x approaches infinity, f(x) approaches 0. i.e.