The value of lim x -x-2 x-tan x is

The correct option is C 0 lim_x →x/2 (sec x tan x ) = lim_h → 0(sec (π/2 h ) tan (π/2 h ) ) = lim_h → 0 (cosec h cot h) = lim_h → 01 cos h/ sin h = li ...

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Byju's Answer

Standard XII

Mathematics

Standard Limits to Remove Indeterminate Form

The value of ...

Question

The value of ${lim}_{x \to \frac{x}{2}} (s e c x - t a n x)$ is

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Solution

The correct option is D
0

${lim}_{x \to \frac{x}{2}} (s e c x - t a n x)$
$= {lim}_{h \to 0} (s e c (\frac{π}{2} - h) - t a n (\frac{π}{2} - h))$
$= {lim}_{h \to 0} (c o s e c h - c o t h)$
$= {lim}_{h \to 0} \frac{1 - c o s h}{s i n h}$
$= {lim}_{h \to 0} \frac{2 s i n^{2} \frac{h}{2}}{s i n h}$
$= l i m_{h \to 0} \frac{2 s i n^{2} \frac{h}{2}}{2 s i n \frac{h}{2} c o s \frac{h}{2}}$
$= {lim}_{h \to 0} t a n \frac{h}{2} = 0$

Suggest Corrections

The value of limx→x2(secx−tanx) is

The correct option is D 0 limx→x2(secx−tanx) =limh→0(sec(π2−h)−tan(π2−h)) =limh→0(cosech−coth) =limh→01−coshsinh =limh→02sin2h2sinh =limh→02sin2h22sinh2cosh2 =limh→0tanh2=0

The value of ${lim}_{x \to \frac{x}{2}} (s e c x - t a n x)$ is