Midterm Examination in Basic Calculus

Use the graph on the right to answer numbers 15 to 18. ___15. Which of the following is true? A. The limit of f(x) as x approaches -1 is f(x) = 2. B. The limit of f(x) as x approaches 3 exist at f(x) = 2. C. The limit of f(x) as x approaches 3 does not exist. D. The limit of f(x) as x approaches 0 does not exist. ___16. What is lim f ( x) ? x  1 A. -4 C. 2 B. -1 D.  ___17. What is f(-1)? A. -1 C. 1 B. 0 D.  ___18. What is lim f ( x) ? x 3 A. 2 C. DNE B. 3 D.  ___19. Using the table of values, what is the estimated value of the limit as x approaches 2? x 1.9 1.99 1.9999 2.0001 2.01 2.1 f(x) 0.2564 0.2506 0.25001 0.24999 0.2494 0.2439 A. 0.25 B. 25 C. DNE D.  ___20. What is the estimated value of the limit in the table? x 3.9 3.99 3.999 4.001 4.01 4.1 f(x) 12.25 12.01 12.00001 11.99999 11.99 11.75 A. 4 B. 12 C. DNE D.  II. Estimate the limit using the given table of values. 1.__________ x -2.1 -2.01 -2.001 -1.999 -1.99 -1.9 f(x) 36.9 36.09 36.009 35.991 35.91 35.1 2.__________ x 4.9 4.99 4.999 5.001 5.01 5.1 f(x) 9.8 9.98 9.998 10.002 10.02 10.2 3.__________ x 1.99 1.999 1.9999 2.0001 2.001 2.01 f(x) 7.9202 7.9920 7.9992 8.0008 8.0080 8.0802 4.__________ x 2.99 2.999 2.9999 3.0001 3.001 3.01 f(x) 44.701 44.970 44.997 45.003 45.030 45.301 5.__________ x 0.9 0.99 0.999 1.1 1.01 1.001 f(x) -0.8 -0.98 -0.998 -1.2 -1.22 -1.222

III. Evaluate the limit of a function using laws of limits. Put your solution inside the box. 1. 3. 5. lim4 x  2 x  3 2 lim 4 x  1 2 2 x 2  3x  1 x 0 x  2 lim x  3 5x  4 2. 4. lim x 2 3 x  18 x 7 lim x 6 2 x  12 IV. Find the limit of the function or state that the limits DOES NOT EXIST. Put your answer inside the box. 1. lim f ( x) 6. lim f ( x) 11. lim f ( x) x 5 x  2 x 3 2. lim f ( x) 7. lim f ( x) 12. lim f ( x) x 5 x 1 x3 3. lim f ( x) 8. lim f ( x) 13. lim f ( x) x5 x 1 x 5 4. lim f ( x) 9. lim f ( x) 14. lim f ( x) x  2 x  2 x 5 5. lim f ( x) 10. lim f ( x) 15. lim f ( x) x  2 x 3 x5