lim n → ∞ n . cos ( π 4 n ) . sin ( π 4 n ) is equal to Options: A . &nbsp π 4 B . &nbsp π 6 C . &nbsp π 9 D . &nbsp π 3

Answer: Option A : A lim x → ∞ n . cos ( π 4 n ) sin ( π 4 n ) = lim n → ∞ n 2 sin π 2 n = π 4

limn→∞n.cos(π4n).sin(π4n) is equal to

Question

$lim n \to \infty n . cos (\frac{π}{4 n}) . sin (\frac{π}{4 n})$ is equal to

Options:

A .

\frac{π}{4}

B .

\frac{π}{6}

C .

\frac{π}{9}

D .

\frac{π}{3}

Answer: Option A
:
A

lim x \to \infty n . cos (\frac{π}{4 n}) sin (\frac{π}{4 n})

= lim n \to \infty \frac{n}{2} sin \frac{π}{2 n}

= \frac{π}{4}

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