Question

nr 10 si 11... măcar unul din ele ... Va rog!!!

Answer 1

10)$\lim_{n \to \infty} \sqrt{an^2+bn+2}+cn=1 \\ \lim_{n \to \infty} \frac{ (\sqrt{an^2+bn+2}+cn)( \sqrt{an^2+bn+2}-cn) }{ \sqrt{an^2+bn+2}-cn }=1 \\ \lim_{n \to \infty} \frac{an^2+bn+2-c^2n^2}{ \sqrt{an^2+bn+2}-cn }=1 \\ \lim_{n \to \infty} \frac{n^2(a-c)+bn+2}{ \sqrt{n^2(a+ \frac{b}{n}+ \frac{2}{c^2}) }-cn }=1 \\ \lim_{n \to \infty} \frac{n(a-c)+b+ \frac{2}{c} }{ \sqrt{a+ \frac{b}{n}+ \frac{2}{c^2} }-c }=1 \\ \frac{a-c}{ \sqrt{a}-c }=0; \frac{b}{ \sqrt{a} -c}=1 \\ a=c;b= \sqrt{a}-c ;si$
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