Is this solution correct

[urban cape]

I divided the numerator by x and the denominator by x^2. Don't know if that is correct

[buoyant spruce]

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[wooden quartz]

The first step should be dividing both by x^2. However, you made two mistakes of the opposite kinds, so it's correct from step 3.

So, you just need to correct the second step.

[urban cape]

Please another question. How you determine with what to divide with?

[wooden quartz]

For limits like this, you divide by the highest power of the numerator and denominator. In this case it's x^2.

[urban cape]

So for this other case I should divide by x^3?

[wooden quartz]

The numerator behaves like x^3, the denominator behaves like x^2, so yes.

[urban cape]

Hey thank you a lot. I have one last thing. Don't know if you can recommend a book or something else for these types of limits?
Thank you again 🙏

[urban cape]

.

[wooden quartz]

Hm... Well, most of the exercises I did were from Demidovich.

I can also send you my lectures if you're interested. They are in Russian, though.

[urban cape]

If you can, yes.

[wooden quartz]

Here you go. In order: calculus, linear algebra, analytic geometry.
Demidovich is available on Libgen.

[urban cape]

Thank you so much 🙏

[unborn musk]

@urban cape has given 1 rep to @wooden quartz