MATH 1000 Final: MATH 1000 Final Exam

• School: Dalhousie University
• Department: Mathematics
• Course: MATH 1000
• Professor: All

Document Summary

The reverse sides of the pages can be used for (unmarked) rough work. 2: find the following limits. (a) lim x. 0 (c) lim x x 4 2 x. 1 cos (e) lim x ln x x. 2. (a) complete the definitions: (i) f(x) is continuous at x = a if lim (ii) the derivative of a function f(x) is f"(x) = lim. 3. (a) find dy dx for the curve x3 + y3 9xy = 0 . [3] (b) find the equation of the tangent to the curve in part (a) at the point (2,4). (simplify as appropriate. ) [2] (c) for what values of x in the interval [0,2 ] does the graph of f(x) = x + 2 cos x have a horizontal tangent: let f(x) = (x2-1)2/3 . [4] (a) what is the domain of f(x) ? (b) find the critical numbers of f(x) .