Question

What is the limit of f (×) as x approaches - infinty

Answer 1

If the degree of numerator and denominator are equal, then limit will be leading coefficient of numerator divided by the leading coefficient of denominator.

So then the limit would be 3/1 = 3.

Alternatively,


`\displaystyle \lim_(x\to\infty)(3x^2+6)/(x^2-4)=\displaystyle \lim_(x\to\infty)(3x^2+6)/(x^2-4)\cdot(1/x^2)/(1/x^2)=\lim_(x\to\infty)\frac{3+\frac6{x^2}}{1-\frac4{x^2}} = (3+0)/(1-0)=\boxed{3}`

Hope this helps.