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*expires 2/11*) Use`Maple`to write as a product of*exact*linear factors. By exact, I mean you should leave any non-rational factors expressed as radicals; do not approximate terms like as 1.73205, etc. - (
*expires 2/11*) Draw a graph showing both and its fifth Taylor polynomial (that is, ) for between and . What degree of Taylor polynomial seems to be needed to get good agreement in this range''*Hint: use a variation of the command*`convert(taylor(cos(x),x,5),polynom)`to make this work. Think of a suitable way to demonstrate that the approximation you have taken is ``good''- what is a good definition of ``good'' here? - (
*expires 2/18*) Consider the planar curve defined by . Using**only**`Maple`, find the slope of the tangent line to the curve at . Then plot the curve and the tangent line on the same graph.

*Hint: you might want to use*`implicitplot`from the library`plots`. You might find`implicitdiff`helpful, too. - (
*expires 2/18*) Plot the function , for . Find all the zeros of the function with an accuracy of 20 decimal digits.*Hint: See*`Digits`,`fsolve`. - (
*expires 2/18*) Define a`Maple`function that, given a positive integer yields the sum of the first primes. What is such that but ? You might find`sum`and`ithprime`helpful. - (
*expires 2/18*) Use the Taylor expansion of near the point to compute the value of to 30 places. How many terms are needed to compute the value to 50 places?