Limx -0 - sin - 12x-tan - 13x - -

[ lim_x →0^ + sin^ 12x/tan^ 13x; #160;= lim_x →0^ + 2xsin^ 12x/2x.1/3xtan^ 13x/3x; #160;= 1 × 2/1 × ...

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Basic Inverse Trigonometric Functions

limx →0 + sin...

Question

$lim x \to 0^{+} \frac{{sin}^{- 1} 2 x}{{tan}^{- 1} 3 x} = ?$

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lim x \to 0 \frac{\sqrt{1 + {tan}^{- 1} 3 x} - \sqrt{1 - {sin}^{- 1} 3 x}}{\sqrt{1 - {sin}^{- 1} 2 x} - \sqrt{1 + {tan}^{- 1}} 2 x} =

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{tan}^{- 1} 2 x + {tan}^{- 1} 3 x = \frac{π}{4}

lim x \to 0 \frac{x}{{tan}^{- 1} 2 x}

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