I'm sure this is easy for the most of...

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I'm sure this is easy for the most of you, but i'd just like to know how i get from the first step to the other. Thanks in advance!

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Format might be weird, but I'll try my best.

As a rule with limits, you can extract constants. So (x^2)/(-x * ln(3)) has the constant [-ln(3)] in the denominator

Rewrite it as (x^2)/(x) * (-1)/(ln(3))

And extract the constant to the front of the limit, and simplify the limit to x {x =\= 0} and viola.

You are left with the second step

Hope this helped.

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>>7807305

Cancel out the x and pull out the constant.

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>>7807305

It's just a property of limits [eqn] \lim_{ x \to a } c f(x) = c \lim_{x \to a} f(x) [/eqn] Which if you think about it makes a lot of sense. So in this problem [eqn] \lim_{x \to 0^{+}} - \frac { x^2 } { x \ln (3) } = - \frac { 1 }{ \ln(3) } \lim_{x \to 0^{+}} x [/eqn] Where the last equality is just the application of the above property and cancellation of x.

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>>7807305

>>7807332

Thank you so much! while we are at this mind to help me with this anti-derivative?

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>>7807341

(ln(2-3x^2))/-6

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>/sci/ - Teens fresh out of Calc I do Chad's homework because this is the only validation they will ever feel in their sad lives

Pretty good prep for sucking off business grads in your future STEM-monkey careers I suppose.

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>>7807326

This is correct. X is a factor on the top and bottom of the fraction, so it can be pulled out as X/X or 1. Then we can pull out -1/ln3 because it is not reliant on X. If it were -X^2/XlnX, it would simplify to -X/lnX and you could not pull out the -1/lnX term.

I hope that makes some sense.

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>>7807341

[math] - \frac{1){6} sin^{-1}(\frac{3x^2}{2}) [/math]

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[math] - \frac{1){6} sin^{-1}(\frac{3x^2}{2})[/math]

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>>7807341

- \frac{1}{6} sin^{-1}(\frac{3x^2}{2})

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>>7807341

[math] - \frac{1}{6} sin^{-1}(\frac{3x^2}{2}) [/math]

I'm retarded

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