Question by maya: CaLCULUS!!?
evaluate
lim (ln(x^50)) / x^100
x->infinity

show full solution please

Best answer:

Answer by Chris
This is a L’Hopital’s Rule question. You can see that normal evaluation gives you ∞/∞ , an indeterminate form.

So first do something that’ll make this easier: change ln(x^50) to 50lnx (logarithmic rules allow you to do this).

You have the limit of 50lnx / x^100 .

Take the derivative of both the top and the bottom (NOT the whole expression):

[50/x] / [100x^99] = 1/2x^100 .

The limit of this expression as x goes to ∞ is more clearly 0.

So your answer is 0.

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