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Maths-

General

Easy

Question

$L t subscript y not stretchy rightwards arrow 0 end subscript fraction numerator sin invisible function application left parenthesis a plus b x right parenthesis minus sin invisible function application left parenthesis a minus b x right parenthesis over denominator x end fraction$

$2 b \cos a$
$2 b \sin a$
$2 \cos a$
$2 \sin a$

hint Hint:

In the question first we will use L hospital theorem. Then we can put the value of x to get the answer.

The correct answer is: $2 b cos space a$

$L t subscript y not stretchy rightwards arrow 0 end subscript fraction numerator sin invisible function application left parenthesis a plus b x right parenthesis minus sin invisible function application left parenthesis a minus b x right parenthesis over denominator x end fraction$
using L hospital theorem,
$limit as x rightwards arrow 0 of fraction numerator begin display style fraction numerator d sin left parenthesis a plus b x right parenthesis over denominator d x end fraction end style minus begin display style fraction numerator d sin left parenthesis a minus b x right parenthesis over denominator d x end fraction end style over denominator begin display style fraction numerator d x over denominator d x end fraction end style end fraction equals limit as x rightwards arrow 0 of fraction numerator b. cos space left parenthesis a plus b x right parenthesis plus b. cos space left parenthesis a minus b x right parenthesis over denominator 1 end fraction equals b. cos left parenthesis a plus b.0 right parenthesis plus b. cos left parenthesis a minus b.0 right parenthesis equals b. cos space a plus b. cos a equals 2 b. cos a$

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