MATH 221 Midterm: Kansas State MATH 221 221fxu94

• School: Kansas State University
• Department: Mathematics
• Course: MATH 221
• Professor: All

Document Summary

Do not simplify and show all work. (30pts) 1. Find the derivatives of the following functions. (a) f (x) = ln[cos(x2 + 1)] (b) f (x) = (ex2. 2 (c) g(x) = x x (10pts) 2. f (x) = x x 1 has an inverse, what is it? page 2 (10pts) 3. Z ln x x dx page 4 (b) Z x2 + 1 + x 1 x1/2 dx (30pts) 6. Investigate each of the following series for convergence. page 5 (a) Find the maclaurin series associated with f (x) = sin 2x page 6 (10pts) 8. Use the binomial series to nd the maclaurin series representa- tion of f (x) = 1 (1 x)2 . page 7 (10pts) 10. Find the vertex, axis, focus, and directrix of x = 4y + y2 . page 8 (10pts) 11. Find the rectangular coordinates of the point ( 1, 3 ) .