Question

Salut! Cine poate sa ma ajute la limita asta?

Answer 1

$lim \frac{3 \times 5 {}^{n} + 4 \times {3}^{n} }{3 \times 3 {}^{n} + 3 {}^{2} \times 3 {}^{n} } = \\ \\ = lim \frac{5 {}^{n} (3 + 4 \times ( \frac{3}{5}) {}^{n}) }{3 \times 3 {}^{n} + 9\times {3}^{n}} =$

(3/5)^n tinde spre 0

$= lim \frac{3 \times {5}^{n} }{12 \times 3 {}^{n} } = \\ \\ = \frac{3}{12} lim( \frac{5}{3} ) {}^{n} = \\ \\ = \frac{1}{4} \times \infty = \\ \\ = \huge{ \infty }$