MATH 201 Notes Formulas, Fall 2012

Additional problems from previous quizzes (Math 201 quiz2) Prof. H. Abu-Khuzam 1. Let f(x,y)= . At what points (x,y) is the function f continuous? Explain 2. Show that does not exist 3. Find the first four terms of the binomial series for the function . 4. Decide whether the following limit exists 5. Use Maclaurin series to estimate the integral with an error of magnitude less than 0.001 6. Let Find 7. Find . Explain Circle the correct answer in each of the following problems [ 5 points for each correct answer, -1 point penalty for each wrong answer]. 8. (a) 1 (b) 1/2 (c) 0 (d) does not exist [5 pts.] 9. The surface is a (A) elliptic paraboloid (B) elliptic cone (C) circular paraboloid (D) hyperbolic paraboloid (E) none of the above 10. Consider the function f(x,y) = . Then (A) f is discontinuous at (0,0) for all values of k. (B) f is continuous at (0,0) provided that k=0 (C) f is continuous at (0,0), provided that k=1 (D) f is continuous at (0,0) , provided that k=1. (E) f is continuous at (0,0) for all values of k. 11. If the equation xexy + yezx + zexy =2, determines z as a function of x and y, then at ( 0, 1, 1) is equal to: (a) 0 (b) 1 (c) 3 (d) -3 (e) none of the above 12. Using the Maclaurin series for , the Maclaurin series of is (A) (B) (C) (D) (E) none of the above 13. = (a) (b) 1 (c) 0 (d) -1 (e) does not exist 14. Using series, the value of the is (A) e (B) -3 (C) 3 (D) 0 (E) none of the above 15. If , then (a) (b) (c) limit (d) limit (a) none of the above.