Limit solving (limit at infinity of a rational function)

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Example of solving a limit that goes to infinity of a rational function.

#calculus #limits

Hebert Engineering

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The biggest struggles in calculus is not even the calculus concepts it’s the algebra 😂 gotta get strong with the fundamentals before tackling something that takes it multiple steps forward.

harambe

im studying for finals tomorrow and u just saved me. THANK YOU

lovestein

The expression is NOT a rational function. A rational function is an expression that is the ratio of two polynomials. You have a radical in your expression, hence NOT a rational function.

dowmanvarn

You can also omit the non-leading terms.

Inspirator_AG

You can just take the limit as x—> ∞ [sqrt(4x⁶)/-x³ ] and this gives us

2x³/-x³= -2

Algebrainiac

Can’t we just use the shortcut since they technically have the same degree and do 2x^3/-x^3 and get our answer that way

SackbotNinja

Or you can use Trocino Method and eliminate and only use the controlling factors.

willisilikefood

YOUR VOICE MAKES ME WANT TO CLEARR MY THROAT AGAIN AND AGAIN WTF

JM-neep

How is it 4 in top after multiplying x^3??? Would it be 4x^3???

Delicious.Meiloorun

And this should be the horizontal asymptote

uneducatedseinor

Your method fails if you take the limit of the same function to -infinity. You have to be more careful then that sqrt(x^6) = |x^3| not x^3.

douglaszare

Your voice... Your voice sounds like Rick in Rick and Morty

ronscomic

Calc is easy I just suck at the algebra part when it comes to complex problems

aqua__infinity

is it in indeterminant form when it is infinity/-infinity?

elephantseal

I reason that the 1 and the 2 become irrelevant so get rid of them then simplify to -2

RMF

This is not correct at all. The limit is -2 only when the x approaches +infinity. Otherwise, when x approaches -infinity the limit goes to +2. You can see it by graphing the function or you can factor 4x^6 inside the square root and then bringing the factor out leaving with |2x^3|. So, since we have to different values the limit as x approaches infinity does not exist.

Uskebasa

Only applies to algebraic only polynomials

tonatiuhdeleon

why you not simplify the root
It will be 1+2x^3

You have
2x cube up and -x cube down

Use the rule and Divide to get -2

Don’t miss the absolute

zayed

why is the square root of 1 +x^6 is the same as x^3????

duf

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