`lim_(x->oo) ln(sqrt(x))/(x^2)` Find the limit. Use l’Hospital’s Rule where appropriate. If there is a more elementary method, consider using it. If l’Hospital’s Rule doesn’t...

`lim_(x->oo) ln(sqrt(x))/(x^2)` Find the limit. Use l’Hospital’s Rule where appropriate. If there is a more elementary method, consider using it. If l’Hospital’s Rule doesn’t apply, explain why.

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Chapter 4, 4.4 - Problem 20 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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gsarora17 | (Level 2) Associate Educator

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`lim_(x->oo)(lnsqrt(x))/x^2`

Apply L'Hospital rule , Test L'Hospital condition:`oo/oo`

`=lim_(x->oo)((lnsqrt(x))')/((x^2)')`

`=lim_(x->oo)((1/sqrt(x))(1/2)(x^(-1/2)))/(2x)`

`=lim_(x->oo)((1/(2x))/(2x))`

`=lim_(x->oo)(1/(4x^2))`

apply infinity property,

`=1/oo=0`

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