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olga nikolaevna [1]
3 years ago
11

Evaluate the limit of lim/n->infinity 6n^2+5/3n^2

Mathematics
2 answers:
castortr0y [4]3 years ago
6 0

we are given

\lim_{n \to \infty} \frac{6n^2+5}{3n^2}

we can see that

degree of numerator = degree of denominator =2

so, we can divide both numerator and denominator by n^2

and we get

\lim_{n \to \infty} \frac{(6n^2+5)/n^2}{(3n^2/n^2)}

\lim_{n \to \infty} \frac{(6n^2/n^2)+(5/n^2)}{(3n^2/n^2)}

now, we can simplify it

\lim_{n \to \infty} \frac{6+(5/n^2)}{3}

now, we can plug n=inf

=  \frac{6+(5/(\infty))}{3}

=  \frac{6+0}{3}

=  \frac{6}{3}

=  2...............Answer

nikdorinn [45]3 years ago
5 0

\displaystyle \lim_{n\to \infty} \dfrac{6n^2+5}{3n^2 }=\\\\ \lim_{n\to \infty} \dfrac{n^2\left(6+\dfrac{5}{n^2}\right)}{3n^2 }=\\\\ \lim_{n\to \infty} \dfrac{6+\dfrac{5}{n^2}}{3}=\\\\ \dfrac{6+0}{3}=2

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