For x - 0- -2 Find limx - 0 - 3x-2 sin x - tan x - where - denote the greatest integer function-

The correct option is A 1 Consider #160; f(x)=3x2sin x+tan x =32sin xx+tan xx x→ 0lim f(x) #160; =x→ 0lim (32sin xx+tan xx) = ...

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For x ϵ 0,...

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For x $ϵ (0, \frac{π}{2})$ Find $lim x \to 0 [\frac{3 x}{2 sin x + tan x}]$ , where [.] denote the greatest integer function.

1

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0

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2

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lim x \to \frac{π}{2} \frac{sin x}{{cos}^{- 1} [\frac{1}{4} (3 sin x - sin 3 x)]}

{lim}_{x \to \frac{π}{2}} \frac{s i n x}{c o s^{- 1} [\frac{1}{4} (3 s i n x - s i n 3 x)]}

f (x) = ⎧ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} [\frac{2 (sin x - {sin}^{3} x) + ∣ ∣ sin x - {sin}^{3} x ∣ ∣}{2 (sin x - {sin}^{3} x) - ∣ ∣ sin x - {sin}^{3} x ∣ ∣}], x \neq \frac{π}{2} f o r x \in (0, π) 3 x = \frac{π}{2} \end{matrix}

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f (x) = [tan x] + \sqrt{tan x - [tan x]}, 0 \leq x < \frac{π}{2}

[.]

f (x) = \frac{x (sin x + tan x)}{[\frac{x + π}{π}] - \frac{1}{2}}

x \neq n π

[]

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