`lim_(x->oo) ln(x)/sqrt(x)` 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,...

`lim_(x->oo) ln(x)/sqrt(x)` 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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Textbook Question

Chapter 4, 4.4 - Problem 17 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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gsarora17's profile pic

gsarora17 | (Level 2) Associate Educator

Posted on

`lim_(x->oo)ln(x)/sqrt(x)`

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

`=lim_(x->oo)((ln(x))')/((sqrt(x))')`

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

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

plug in the value,

=2/`oo`

`=0`

scisser's profile pic

scisser | (Level 3) Honors

Posted on

Use LH's rule

`lim_(x-gtoo)((1/x)/(1/(2sqrtx)))`

Simplify,

`lim_(x-gtoo)(2/sqrtx)`

square root of infinity is still infinity. 2 divided by a really big number (like infinity) is just 0.

`=0`

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