MATH 1A Final: MATH 1A Harvard 1a Final 2004 Spring
Document Summary
Full credit may not be given for an answer alone. You may use the backs of the pages or the extra pages for scratch work. Students who, for whatever reason, submit work not their own will ordinarily be required to withdraw from the college. 1: (15 points) find the following limits. (i) lim x . 2: (20 points) find the derivatives of the following functions. (i) f (x) = x3 (ii) f (x) = 3x. 3: (15 points) a sh tank is to be designed with square base and rectangular sides (and no top). The material for the base costs ve times as much as the glass for the sides. 4 (15 points) 1 is a pretty lousy approximation to 3 2. 4. method, nd a rational number (whole number or fraction) which is closer, and another one which is still closer.
