limit

2 Answers

apply LH rule...

1+2x3(ln x)² 1x

= x+2x²3(ln x)²

again apply LH rule

= 1+4x6(ln x)/x

= x+4x²6(ln x)

= 1+8x6/x

= x+8x²6

which seems to be infinite !

or, put logx=t

or we have

limxâ†’âˆž (1+e^t+e^2t)/t³

= [1+(1+t+t²/2+t³/6+...)+(1+2t+2t²+8t³/6...)]/t³

=3/t³ +3t/t³ + 5t²/2t³ + 3/2 + (powers of t more than 3)/t³

=âˆž

cheers!!

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