Instructions: Solve the following. You may use your books and notes Without odor permission. the scores for late umbers will be lowered Show all your world 80% of your score is for correct justified answers; 20% is for correct and clear presentation. For the graphing problems, use www.desmos.com/calculator and you must demonstrate how graphing can be accomplished using what you learned in calculus. I will accept only Desmos graphs. Email or share your graphs with me. Well-documented graphs with additional features included that demonstrate the concepts will receive extra credit. 1. Graph each of the following. Find the range of angles that trace out the full graph. Determine and graph the equations of the tangent lines at each relative maximum of r. This example might be helpful hnos://www.desmos.comicalculatorNdim zrm50 s https://www.desmos.com/calculator/ogu7bi9aug a. r = 1 — 2cos(8)b. r = 1 + sin(58/2) C. r = 1 + 2 sin(28/5) d. r = 2sin(88) — cos(8) e. r = 8 + 3csc(0) f. r = cos2(561)+ sin(30) + 0.3 2. Determine whether the following converge. a. For each of the following use three tests I. En=i 0 1 or equivalently Ert.i nP: p < —1 als iii.En=j7n : p = 1 or equivalently atinP: p = -1 Es=1 b. Ertl ts 71=2 L Ertl 07.1)-60:5) c. Ln=1.n..4224 ant —3n vo, 1 U. Ln=1,3n_4 nr4 n. Ermid + 1)2 e.atin,nn+4 o. Errs ne -/12 f. Eni=s sin(1) p. Enc...=1 snsis2(ss) 44+coszoo sin((2n+1.4) g. sinOsn+.0i5 h. EZ=1( 1?n n 05+0 3. Let z — Using the de Moivre's formula, find (express you answers in em and a+bi form) a. z2 b. z3 c. zit d. z5 e. z6 4. Find the 11th roots of 1; that is all solutions to x"=1 again using de Moivre's formula.
12 years ago