Evaluate displaystyle lim x arrow ∞ 2x-1 tan ((a/2x)).

Question

Evaluate displaystyle lim x arrow ∞ 2x-1 tan ((a/2x)). (A) a (B) 2 a (C) (a/2) (D) 4 a

Tardigrade Admin · Accepted Answer

We have displaystyle lim x arrow ∞ 2x-1 tan ((a/2x))= displaystyle lim x arrow ∞ (a/2) ( tan ((a/2x))/((a)2x))((0/0). form ) =(a/2) lim y arrow 0 ( tan y/y)=(a/2) (where y=(a/2x) )

Q. Evaluate $x \to \infty lim 2^{x - 1} tan (\frac{a}{2 ^{x}})$ .

a

2 a

$\frac{a}{2}$

4 a

We have
$x \to \infty lim 2^{x - 1} tan (\frac{a}{2 ^{x}}) =< b r / >< b r / > x \to \infty lim \frac{a}{2} \frac{tan ( \frac{a}{2 ^{x}} )}{( \frac{a}{2 ^{x}} )} (\frac{0}{0}$ form $)$
$= \frac{a}{2} lim_{y \to 0} \frac{t a n y}{y} = \frac{a}{2}$
(where $y = \frac{a}{2 ^{x}}$ )

Q. Evaluate x→∞lim​2x−1tan(2xa​).

a

2 a

2a​

4 a

We have x→∞lim​2x−1tan(2xa​)=<br/><br/>x→∞lim​2a​(2xa​)tan(2xa​)​(00​ form ) =2a​limy→0​ytany​=2a​ (where y=2xa​ )

Q. Evaluate $x \to \infty lim 2^{x - 1} tan (\frac{a}{2 ^{x}})$ .

$\frac{a}{2}$

We have
$x \to \infty lim 2^{x - 1} tan (\frac{a}{2 ^{x}}) =< b r / >< b r / > x \to \infty lim \frac{a}{2} \frac{tan ( \frac{a}{2 ^{x}} )}{( \frac{a}{2 ^{x}} )} (\frac{0}{0}$ form $)$
$= \frac{a}{2} lim_{y \to 0} \frac{t a n y}{y} = \frac{a}{2}$
(where $y = \frac{a}{2 ^{x}}$ )