Determine the asymptote of the function f?

Hey, I'm currently practicing math and it's actually going really well. I'm just making a logical error and I'm stuck. Can someone tell me exactly how to get -(0.25x^2+x) and then calculate below it? I'm probably just overthinking it. Thanks in advance!

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Willy1729
1 year ago

Hello,

in the polynomial division you consider the x-member (or how the variable may be) with the highest potency.

Divide 0.25×2-2x-3 by 0.5x+2, you need to multiply 0.5x to 0.25×2. This is of course 0.5x and thus the first part of the result.

Now you multiply 0.5x with 0.5x+2, which gives 0.25×2+x, and remove it from 0.25×2-2x. This disappears 0.25×2 and it remains -3x. Now you get the -3 as in the written division of multi-digit numbers and now
-3x-3 by 0.5x+2. 0.5x*(-6)=-3x and (-6)*(0.5x+2) gives -3x-12.

This is also removed again, so that now also -x disappears and 9 remains. Since there are no further terms in the dividend, 9/(0.5x+2) remains as the remainder, which goes against zero for x.

Bevel asymptote is thus -0.5x-6, i.e. the result of the division without the remainder, which goes against zero and disappears.

Best regards,

Willy

Willy1729
1 year ago
Reply to  Willy1729

Thank you for the star.

Willy