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) = a0xm + a1xm-1 + a2xm-2 + ….. + am-1x + am
And f(x) = b0xn + b1xn-1 + b2xn-2 + ….. + bn-1x + bn
Dividing numerator and denominator by xm we get
→ = ∞ [∵ m > m – 1 > …. > m – ( ...