Calculate these limits. If the limit is oo or-oo, write infinity or - infinity. If the limit does not exist, write DNE: Hint: Remember the first thing you check when you are looking at a limit of a quotient is the limit value of the denominator. quotient 1. If the denominator does not go to 0, you should be able to right down the answer immediately. 2. If the denominator goes to 0, but the numerator does not, you will have to check the sign (+) of the quotient, from both sides if the limit is not one-sided. 3. If both the numerator and the denominator go to 0, you have to do the algebraic trick of rationalizing. So, group your limits into these three forms and work with them one group at a time. (a) lim t-pl/2 sint-sin2t+17cos 2 t 2cos 2 t = (b) lim sint + sin 2t+17cos 2 t, t-pl/2 2cos 2 t (c) lim cost-sin2t+ 17cos 2 t t-pi/2 2cos 2 t (d) lim t-pl/2 cost + sin t + 17cos t 2cos 2t (e) lim t-pi/2 sint-sin 2t+ 17cos 2sin 2 t 2 t (f) lim t-pl/2 (9) lim t-pl/2 (h) lim sint + sin 2t+17cos 2 t 2sin 2t cost-sin2t+17cos 2 t, 2sin 2t cost+ sin 2t+ 17cos 2 t 2sin 2 t sint-sin2t+17cos 2 t 2cos t t-pi/2 (i) lim t-pi/2 () lim sint+sin2t+17cos 2 t t-pl/2 2cos t (k), lim cost-sin2t+17cos 2 t, t-pl/2 2cos t =