Pre-Calc Homework Solutions 359

4 dx x 2 16 lim tan b t 1 4t dt t 2t 1t 2 1 dt t2 dt

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: dt t 1 2t t 2 4 2 1 dt 1 1 dt t2 1 2 2 2 1 2 2t dt t2 1 49. Use the limit comparison test with f( ) g( ) 1 f( ) g( ) 1 and 1 . Both are positive continuous functions on [1, ). 2 2 ln t ln 3 1 2 ln t tan 1 t C tan 1 t C lim lim 1 1 1 lim 1 1 2 1 (t 1) t2 1 1 Since g( ) d d b t 1 4t dt t 2(t 1)(t 2 1) 1 lim 0 1 1 1/2 1 t 1 4t dt t 2(t 1)(t 2 1) 4t 3 t 1 dt t (t 1)(t 2 1) 2 3 3 t 1 4t dt t 2(t 1)(t 2 1) 4t 3 t 1 dt t (t 1)(t 2 1) 2 3 3 b 1 d b lim ln b 1 1/2 0 2 1 lim ln b b t 1 4t dt t 2(t 1)(t 2 1) 2 t 1 4t dt t 2(t 1)(t 2 1) , we know that 1 g( ) d diverges and so 1 f( ) d diverges. This means that the given integral diverges....
View Full Document

This note was uploaded on 10/05/2011 for the course MAC 1147 taught by Professor German during the Spring '08 term at University of Florida.

Ask a homework question - tutors are online