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

Answer:

$\frac{1}{5}$

Step-by-step explanation:

Given the expression;

$\lim_{x \to \infty} \dfrac{x+x^2}{5x^2}$

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

$\lim_{x \to \infty} \dfrac{\frac{x}{x^2} +\frac{x^2}{x2}}{\frac{5x^2}{x^2} }\\ \lim_{x \to \infty} \frac{\frac{1}{x}+ 1 }{5}\\As \ x \ tends \ to \ \infty, \ \frac{1}{x} \ tends \ to \ zero. \ Hence;\\ \lim_{x \to \infty} \frac{\frac{1}{x}+ 1 }{5} = \frac{0+1}{5}\\= \dfrac{1}{5}$

Hence the limit of the function as x tends to infinity is $\frac{1}{5}$