Unformatted text preview: x 2 8 + x 3 16(1+ tx ) 5 / 2 , t ∈ (0 , 1). 5. By l’Hopital’s rule lim h → f ( a + h ) + f ( ah )2 f ( a ) h 2 = lim h → f ( a + h )f ( ah ) 2 h = f 00 ( a ) . 6. (a) No, since lim n →∞ a n 6 = 0. (b) Yes. Comparison test: √ n +1√ n n = 1 n ( √ n +1+ √ n ) < 1 n 3 / 2 . (c) Yes. Use d’Alembert’s test. 7. (a) Comparison test and deﬁnition of the absolute convergence. (b) Note that  a n x n  ≤ a n . Then use comparison test. 1...
View
Full Document
 Winter '10
 Spyros
 Calculus, Mean Value Theorem, lim

Click to edit the document details