Learning Guide Learning Guide

5.2 Assumptions • 1650The following limit depends on b.> limit(b*x, x=infinity);signum(b) ∞> assume( b>0 );> limit(b*x, x=infinity);∞You can use infolevel to have Maple report the details of commandoperations.> infolevel[int] := 2;infolevel int := 2> int( exp(c*x), x=0..infinity );int/cook/nogo1:Given IntegralInt(exp(c*x),x = 0 .. infinity)Fits into this pattern:Int(exp(-Ucplex*x^S1-U2*x^S2)*x^N*ln(B*x^DL)^M*cos(C1*x^R)/((A0+A1*x^D)^P),x = t1 .. t2)Definite integration: Can’t determine if the integral isconvergent.Need to know the sign of --> -cWill now try indefinite integration and then take limits.int/indef1: first-stage indefinite integrationint/indef2: second-stage indefinite integrationint/indef2: applying derivative-dividesint/indef1: first-stage indefinite integratione (c x) − 1limx→∞ cThe int command must know the sign of c (or rather the sign of -c).> assume( c>0 );> int( exp(c*x), x=0..infinity );