Prove the schwarz inequality (for any pair of functions):
|(f, g)|≤||f||⋅||g||.
(hint: consider the expression ||f+tg||2, where t is a scalar. this expression is a quadratic polynomial of t. find the value of t where it is a minimum. play around and the schwarz inequality will pop out.)

(a) compute the maclaurin polynomial m2(x) for f(x) = cos x. (b) use the polynomial of part (a) to estimate cos π 12. (c) use a calculator to compute the error made using the estimate from part (b) for the value of cos π 12. remember that the error is defined to be the absolute value of the difference between the true value and the estimate.

Is the square root of 4 plus the square root of 16 rational?

Barbara deposited $300 in the bank. if the bank pays her simple interest at the rate of 4 percent per year, how much money will she have in her account at the end of 9 months?