Calculus 2 (BME,EE & IT) Calculus 2 (BME,EE & IT) Assoc. Prof. Nguyen Dinh Assoc. Prof. Nguyen Dinh International University-HCMC International University-HCMC January, 2010 January, 2010 References References [1] [1] J. Stewart, J. Stewart, Calculus – Early Calculus – Early transcendentals (sixth edition) transcendentals (sixth edition) Thomson, Thomson, 2008. 2008. Exercises of Chapter 1 Exercises of Chapter 1 Section 1 (Sequences) Section 1 (Sequences) Exercises of Chapter 1 (cont’d) Exercises of Chapter 1 (cont’d) Hint (for Ex. 57) * If |r|> 1. The sequence is divergent. When |r|< 1, 0<r<1, Hint (for Ex. 57) * If |r|> 1. The sequence is divergent. When |r|< 1, 0<r<1, write nr^n = n/(1 + p)^n with p > 0. Prove write nr^n = n/(1 + p)^n with p > 0. Prove n/(1 + p)^n < (2^2 .2!)/(p^2).n^(1-2). n/(1 + p)^n < (2^2 .2!)/(p^2).n^(1-2). Exercises of Chapter 1 Exercises of Chapter 1 Section 2 (series) Section 2 (series) (Example 6 will be used in Exercise 63 in the next page) (Example 6 will be used in Exercise 63 in the next page) . with p > 0. Prove write nr^n = n/(1 + p)^n with p > 0. Prove n/(1 + p)^n < (2^ 2 .2! )/(p ^2) .n^(1 -2) . n/(1 + p)^n < (2^ 2 .2! )/(p ^2) .n^(1 -2) . . Calculus 2 (BME,EE & IT) Calculus 2 (BME,EE & IT) Assoc. Prof. Nguyen Dinh Assoc. Prof. Nguyen