The value of displaystyle lim m arrow ∞( cos (x/m))m is

Question

The value of displaystyle lim m arrow ∞( cos (x/m))m is (A) 1 (B) e (C) e-1 (D) none of these

Tardigrade Admin · Accepted Answer

displaystyle lim m arrow ∞( cos (x/m))m= displaystyle lim m arrow ∞[1-(1- cos (x/m))]m = displaystyle lim m arrow ∞[1-2 sin 2 (x/2 m)]m =e displaystyle lim m arrow ∞-2 sin 2 (x/2 m) ⋅ m=1

Q. The value of $m \to \infty lim (cos \frac{x}{m})^{m}$ is

$1$

$e$

$e^{- 1}$

none of these

$m \to \infty lim (cos \frac{x}{m})^{m} = m \to \infty lim [1 - (1 - cos \frac{x}{m})]^{m}$
$= m \to \infty lim [1 - 2 sin^{2} \frac{x}{2 m}]^{m}$
$= e^{m \to \infty lim - 2 sin^{2} \frac{x}{2 m} \cdot m} = 1$

Q. The value of m→∞lim​(cosmx​)m is

1

e

e−1

none of these

m→∞lim​(cosmx​)m=m→∞lim​[1−(1−cosmx​)]m =m→∞lim​[1−2sin22mx​]m =em→∞lim​−2sin22mx​⋅m=1

Q. The value of $m \to \infty lim (cos \frac{x}{m})^{m}$ is

$1$

$e$

$e^{- 1}$

$m \to \infty lim (cos \frac{x}{m})^{m} = m \to \infty lim [1 - (1 - cos \frac{x}{m})]^{m}$
$= m \to \infty lim [1 - 2 sin^{2} \frac{x}{2 m}]^{m}$
$= e^{m \to \infty lim - 2 sin^{2} \frac{x}{2 m} \cdot m} = 1$