Lim x -sin 2-3 n -2-3nn - N -A- -B- -C- Does not existD- 0

The correct option is D 0x →∞limsin(2+√(3))^n π/(2 √(3))^n (nϵ N) =x →∞limsin(2+√(3))^n π/(2 √(3))^n×(2+√(3))^n π/(2 √(3))^n =x →∞limsin(2+√(3))^n π/(2 √(3)) ...

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Byju's Answer

Standard XII

Mathematics

Second Fundamental Theorem of Calculus

lim x →∞sin 2...

Question

$l i m x \to \infty \frac{s i n (2 + \sqrt{3})^{n} π}{(2 - \sqrt{3})^{n}} (n ϵ N) =$

0

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- π

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Solution

The correct option is A $0$
$l i m x \to \infty \frac{s i n (2 + \sqrt{3})^{n} π}{(2 - \sqrt{3})^{n}} (n ϵ N) = l i m x \to \infty \frac{s i n (2 + \sqrt{3})^{n} π}{(2 - \sqrt{3})^{n}} \times \frac{(2 + \sqrt{3})^{n} π}{(2 - \sqrt{3})^{n}} = l i m x \to \infty \frac{s i n (2 + \sqrt{3})^{n} π}{(2 - \sqrt{3})^{n}} \times l i m x \to \infty \frac{(2 + \sqrt{3})^{n} π}{(2 - \sqrt{3})^{n}} = 0 \times l i m x \to \infty \frac{(2 + \sqrt{3})^{n} π}{(2 - \sqrt{3})^{n}} [∵ l i m x \to \infty \frac{s i n x}{x} = 0] ∴ L = 0$ .

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limx→∞sin(2+√3)nπ(2−√3)n(nϵN)=

The correct option is A 0limx→∞sin(2+√3)nπ(2−√3)n(nϵN)=limx→∞sin(2+√3)nπ(2−√3)n×(2+√3)nπ(2−√3)n=limx→∞sin(2+√3)nπ(2−√3)n×limx→∞(2+√3)nπ(2−√3)n=0×limx→∞(2+√3)nπ(2−√3)n [∵limx→∞sinxx=0]∴L=0.

$l i m x \to \infty \frac{s i n (2 + \sqrt{3})^{n} π}{(2 - \sqrt{3})^{n}} (n ϵ N) =$