Question

1. Use the Comparison Test to determine whether the integral rinfinity 2/23 - 1dx 2 is convergent or divergent.

2. Determine whether the integral cln(2x)d.2 conveges or diverges. Evaluate the integral in the case that it is convergent

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Answer #1

1) doc oc² -1 2 с Note that > [oc3 - Voca Since ac 2c3 > Vocza Consider C .doc 1203 2 8 il c .doc oc% 11 .doc 32-1 .doc xa aWe know that .doc ½ diverges. 2 test, Hence, By comparison х DIVERGES doc roc² - 1 2 NOTE:- X Sao doc converges if p>1 if p<1So, x. ln (2x).doc = lim x. ln (2x).doc + t =lim (( ln (2x). do اوج ا t 1 .doc =lim tot frente [ 16-05) - Schlenica) ca) - JaIn2. ln (et) -56-3) = lim tot ln 2 t² ln (26) 11 -1 2 lim ta 4 2 07 ln (21) ln ayat. lim 4 2 tot t-2 2 In 2 = xt 2 lim (lon (

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