MAT 131 Midterm: MAT131 Midterm 2 2015 Fall

• School: Stony Brook University
• Department: Mathematics
• Course: MAT 131
• Professor: All

Document Summary

Mat131-fall15- second midterm: (4pts) recall the de nition of a critical point, (4pts) recall the statement of fermat"s theorem, (12pts) sketch the graph of sin 1. Compute the exact value of tan(sin 1(3/5)): (18pts) find the following limits: (a) lim x ln(2 + x) x 1 (b) lim x 2+ 1 x x 2 (c) lim x 0+ x(x2), (d)bonus:(+6pts) lim x 0+ xarcsin(x): (6pts) write the de nition of the derivative of sin at 0 with a limit and deduce, (6pts) here are given two graphs. Which one is the one of f(cid:48) and which one is the one of f ? sin(x) lim x 0 x. Include units in your answer: (24pts) let f be the function de ned by the equation f (x) = ex(x2 4x + 4). Compute limx f (x) and limx f (x).