MATH 75 = CALCULUS I HOMEWORK #3, DUE MONDAY 23 SEPT 2002 ----------------WARREN D. SMITH-------------------------- A) This homework is shorter than usual to give you time to prepare for upcoming QUIZ on MONDAY 23 Sept. See my web page under "quizzes" for description of what will be covered on the quiz, and to get an ungraded PRACTICE QUIZ which is very similar to the real quiz, but a little bit harder (so if you figure out how to ace the practice quiz you should be fine on the real thing). B) COW. I have assigned 12 COW problems on limits. They have to be done by Wednesday 25 sept, but this written homework is due Monday 23 sept. Review of how to connect to COW on the internet (e.g. via my web page): Make yourself a password if first time via PASSWORD EXCHANGE. Do not forget your password. LOGIN with your name and password. HOMEWORK button (& VIEW ASSIGNMENT) will display a list of the assigned problems from COW's "calculus book I". Print out that list (or just keep it in another screen "window"). Then go to COW's MAIN page, hit the book-I button, and navigate thru the menus to reach the assigned problems, then do them. Keep doing them until get them right... if you want credit. It will do the grading, it will instantly tell you if got it right, etc. Do not use browser "back" buttons, use only buttons COW provides, when navigating. You may need to consult your textbook to help, while COWing! That is fine! You can come back and do more COWIng later & it will not forget your previous work! If you ever solve a COW problem, it remembers you solved it forever after. IF YOU CANNOT MANAGE TO USE COW, PLEASE EMAIL ME IMMEDIATELY!! C) Reading. Finish reading chapter 1 of the book and the part pp 60-69 of chapter 2 about limits. Also read all the "useful notes" stuff on my web page (near end). All will be covered on the quiz. So will some precalculus stuff that is not in the book. The web page (see under "quiz\#1") has a better description of exactly what is covered on the quiz. If you want to review some precalculus you might try some un-assigned COW problems in the precalculus COW "book" in areas you feel weak in. Or go to the MSRC or to the TA and get help in those areas. [Precalculus you had better know: how to manipulate fractions, solve quadratics, solve linear equations in a few variables, and the basics of trigonometry.] --------------------------------------------------------------------- 1. Remember, a limit lim F(x) EXISTS if, as x gets closer x-->v and closer to v (no matter how it approaches it), F(x) always gets arbitrarily close to some value L (and then L is the limit). The most usual way in which limits fail to exist is if F(x) has a discontinuous JUMP in value at x>v versus x0 Does this limit exist? Why or why not? (And if it exists, then what is it?) What if we make the approach to 0 be 1-sided, such as x-->0+? 2 2 2. Is ( ( (1+x) (3-x) + 7 + x ) + 9 + x ) a polynomial? Why (or why not)? And if it is, then what is its degree? 2 3. Simplify ( (1+x) (3/x - x) / (7+x) + 9 + x /(x-3) ) to rational (polynomial(x)/polynomial(x)) form. What is the degree of the top, i.e. numerator, polynomial? 4. We know sin(a+b) = sin(a)cos(b) + sin(b)cos(a) and we know a similar addition formula for cosine. Now use this to figure out a formula for sin(3a) in terms of sin(a) and cos(a) ONLY. Then, devise a formula for sin(4a) in terms of sin(a) and cos(a) ONLY. Hint: substitute! -----------------------------------------------------------------