Thread: slant asymptote

show that the curve sqrt(x^2+4x) has two asymptotes: y=x+2 and y+-x-2.

Originally Posted by johntuan

show that the curve sqrt(x^2+4x) has two asymptotes: y=x+2 and y+-x-2.

A 'nasty' way (mathematicians turn away):

.

A much better way is to expand using the generalised binomial theorem and then take the limit.

haha..but i dont understand how +-(x+2) becomes asymptotes?...the way i would get S.A is long division or the limit way...but this one is weird because its not a rational function

Originally Posted by johntuan

haha..but i dont understand how +-(x+2) becomes asymptotes?...the way i would get S.A is long division or the limit way...but this one is weird because its not a rational function

Slant asymptotes are lines that the curve approaches as x --> +oo or x --> -oo. As x --> +oo or -oo, and the square root of this is . This is not a rigorous way of doing it. The mathematicians of MHF will pounce on this and make mince meat of it.

But I'm not sure you're at a level where a rigorous approach would make much sense, so you'll just have to make do with the one above.