MATH 201 Notes Extra Notes, Fall 2015

Math 201 section 10.1 Extra Formulas & Problems Formula 1++: 0 Example : lim ln .0 0 for any ln lim .0 0001      n n c n n n c n Formula 7: 0 ! lim   n n n n (see Exercise 63) Formula 8:     n n n ! lim (Most students think the answer is 1 because .1 lim    n n n ) 1) Great problem: Find n n n n 2) 9 lim (    Fastest Solution: 7 2 9 2) 1( 9) 1( lim 2) 9 lim ( e e e n n n n n n n n n          0 , 00, 1 :   REMINDER are the undefined limits in exponents (why?) (Take their ln) undefined) (!!! 1 3) 1( lim     n n 2) n The answer is ofcourse 3e (by Formula 5). n n n n 2) 9 lim (   3)  = undefined) (!!! 1 The answer here is 7e (see Great problem 1 above) 4) 1 lim 1    n n because we are taking the limit of the sequence 1, 1, 1, 1, 1, ………. The following method in taking limits of exponents is acceptable to me provided we do NOT run into 0 1 , 00,   (the Undefined limits in exponents). For example, 5)        3) (5 2) 3 1 lim ( 5 n n n n 6) 0 5) (3 2) 5 9 lim (3        n n n n