Question

Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider using it. lim xâ[infinity] x + x2 1 â 5x2

Answer 1

`(1)/(5)`

Explanation:

Given the expression;

`\lim_(x \to \infty) (x+x^2)/(5x^2)`

To find the limit of the function, we need to first divide through by the highest degree if x i.e x² as shown;

`\lim_(x \to \infty) ((x)/(x^2) +(x^2)/(x2))/((5x^2)/(x^2) )\\ \lim_(x \to \infty) ((1)/(x)+ 1 )/(5)\\As \ x \ tends \ to \ \infty, \ (1)/(x) \ tends \ to \ zero. \ Hence;\\ \lim_(x \to \infty) ((1)/(x)+ 1 )/(5) = (0+1)/(5)\\= (1)/(5)`

Hence the limit of the function as x tends to infinity is
`(1)/(5)`