The value of limh-0 2-3sin -6-h -cos -6-h -3 h-3cos h-sin h is -

Lim_h→0 2{√(3)sin ( π6+h ) cos ( π6+h nbsp; )√(3) h(√(3)cos h sin h)} =lim_h→0 42√(3){cos ( π6)sin ( π6+h ) cos ( π6+h nbsp; )sin ( π6) h[cos ( π6)cos h ...

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Standard XII

Mathematics

Trigonometric Ratios for Sum of Two Angles

The value of ...

Question

The value of $lim h \to 0 2 ⎧ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎩ \frac{\sqrt{3} sin (\frac{π}{6} + h) - cos (\frac{π}{6} + h)}{\sqrt{3} h (\sqrt{3} cos h - sin h)} ⎫ ⎪ ⎪ ⎪ ⎪ ⎬ ⎪ ⎪ ⎪ ⎪ ⎭$ is :

\frac{3}{4}

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\frac{2}{\sqrt{3}}

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\frac{4}{3}

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\frac{2}{3}

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Solution

The correct option is C $\frac{4}{3}$
$lim h \to 0 2 ⎧ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎩ \frac{\sqrt{3} sin (\frac{π}{6} + h) - cos (\frac{π}{6} + h)}{\sqrt{3} h (\sqrt{3} cos h - sin h)} ⎫ ⎪ ⎪ ⎪ ⎪ ⎬ ⎪ ⎪ ⎪ ⎪ ⎭$
$= lim h \to 0 \frac{4}{2 \sqrt{3}} ⎧ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎩ \frac{cos (\frac{π}{6}) sin (\frac{π}{6} + h) - cos (\frac{π}{6} + h) sin (\frac{π}{6})}{h [cos (\frac{π}{6}) cos h - sin h sin (\frac{π}{6})]} ⎫ ⎪ ⎪ ⎪ ⎪ ⎬ ⎪ ⎪ ⎪ ⎪ ⎭$
$= lim h \to 0 \frac{2}{\sqrt{3}} ⎧ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎩ \frac{sin (\frac{π}{6} + h - \frac{π}{6})}{h (cos (h + \frac{π}{6}))} ⎫ ⎪ ⎪ ⎪ ⎪ ⎬ ⎪ ⎪ ⎪ ⎪ ⎭$
$= lim h \to 0 \frac{2}{\sqrt{3}} ⎧ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎩ \frac{sin (h)}{h cos (h + \frac{π}{6})} ⎫ ⎪ ⎪ ⎪ ⎪ ⎬ ⎪ ⎪ ⎪ ⎪ ⎭$
$= \frac{2}{\sqrt{3}} \times \frac{2}{\sqrt{3}} = \frac{4}{3}$

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Similar questions

lim h \to 0 \frac{2 (\sqrt{3} sin (\frac{π}{6} + h) - cos (\frac{π}{6} + h))}{\sqrt{3} h (\sqrt{3} cos h - sin h)}

is equal to

lim h \to 0 2 ⎡ ⎣ \frac{\sqrt{3} sin (\frac{π}{6} + h) - cos (\frac{π}{6} + h)}{\sqrt{3} h (\sqrt{3} cosh - sinh)} ⎤ ⎦ =

Q. The value of

lim h \to 0 2 ⎧ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎩ \frac{\sqrt{3} sin (\frac{π}{6} + h) - cos (\frac{π}{6} + h)}{\sqrt{3} h (\sqrt{3} cos h - sin h)} ⎫ ⎪ ⎪ ⎪ ⎪ ⎬ ⎪ ⎪ ⎪ ⎪ ⎭

is :

\underset{h \to 0}{\lim 2} \{\frac{\sqrt{3} \sin (π / 6 + h) - \cos (π / 6 + h)}{\sqrt{3} h (\sqrt{3} \cos h - \sin h)}\}

is equal to

(a) 2/3
(b) 4/3
(c)

- 2 \sqrt{3}

(d) −4/3

Find the value of $lim h \to 0 [2 - h] + lim h \to 0 [2 + h]$

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Trigonometric Ratios for Sum of Two Angles

Standard XII Mathematics

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The value of limh→0 2⎧⎪ ⎪ ⎪ ⎪⎨⎪ ⎪ ⎪ ⎪⎩√3sin(π6+h)−cos(π6+h)√3 h(√3cosh−sinh)⎫⎪ ⎪ ⎪ ⎪⎬⎪ ⎪ ⎪ ⎪⎭ is :

The value of $lim h \to 0 2 ⎧ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎩ \frac{\sqrt{3} sin (\frac{π}{6} + h) - cos (\frac{π}{6} + h)}{\sqrt{3} h (\sqrt{3} cos h - sin h)} ⎫ ⎪ ⎪ ⎪ ⎪ ⎬ ⎪ ⎪ ⎪ ⎪ ⎭$ is :