MATH 140 Midterm: MATH140H BOYLE-M FALL2004 0101 MID EXAM

• School: University of Maryland
• Department: Mathematics
• Course: MATH 140
• Professor: All

Document Summary

No books, no notes, no calculators: (a) (5 points) suppose a and l are real numbers and f is a function de ned on an open interval containing a. Give the epsilon-delta de nition of lim x a f (x) = l . (b) (10 points) give an epsilon-delta proof that limx 3 x2 + x = 12. (30 points) evaluate each of the following. 2. number, + , , or does not exist . No proof required. (a) lim x 0 sin(5x) sin(7x) (d) lim x 0 x sin(1/x) (b) lim x e (e) lim x 0 ln(ln(x)) ln(x)) cos(x) x (c) lim x /2+ sec(x) (f ) lim x 0. Then determine whether whether the following function is continuous at x = 1. f (x) = 2x + 1.