When *x* tends to infinity the limit is called limit at infinity. Let us first discuss the limit of the form to be found such that *f*(*x*), *g*(*x*) → ∞ as *x* → ∞, where *f*(*x*) and *g*(*x*) are polynomials of degree *m* and *n* respectively.

Let *f*(*x*) = *a*_{0}*x*^{m} + *a*^{1}*x*^{m-1} + *a*_{2}*x*^{m-2} + ….. + *a*_{m-1}*x* + *a*_{m}

And *f*(*x*) = *b*_{0}*x*^{n} + *b*_{1}*x*^{n-1} + *b*_{2}*x*^{n-2} + ….. + *b*_{n-1}*x* + *b*_{n}

Dividing numerator and denominator by *x*^{m} we get

→ = ∞ [∵ *m* > *m* – 1 > …. > *m* – ( ...

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