1003047401 | math4u.vsb.cz

SubArea:

Limit of a sequence

Level:

Project ID:

1003047401

Accepted:

1

Clonable:

0

Easy:

1

Choose the correct formula to calculate the limit.

L = lim_{n \to \infty} \frac{3 \cdot 5^{n} + 2 \cdot 6^{n}}{2 \cdot 5^{n} + 4 \cdot 7^{n}}

L = lim_{n \to \infty} \frac{3 \cdot {(\frac{5}{7})}^{n} + 2 \cdot {(\frac{6}{7})}^{n}}{2 \cdot {(\frac{5}{7})}^{n} + 4} = 0

L = lim_{n \to \infty} \frac{3 \cdot {(\frac{5}{6})}^{n} + 2}{2 \cdot {(\frac{5}{7})}^{n} + 4} = \frac{1}{2}

L = lim_{n \to \infty} \frac{3 + 2 \cdot {(\frac{6}{5})}^{n}}{2 + 4 \cdot {(\frac{7}{5})}^{n}} = \frac{3}{2}

L = \frac{3 \cdot 5^{\infty} + 2 \cdot 6^{\infty}}{2 \cdot 5^{\infty} + 4 \cdot 7^{\infty}} = \infty

L = lim_{n \to \infty} \frac{3 \cdot {(\frac{5}{7})}^{n} + 2 \cdot {(\frac{6}{7})}^{n}}{2 \cdot {(\frac{5}{7})}^{n} + 4 \cdot {(\frac{7}{7})}^{n}} = \frac{5}{6}