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Question

Evaluate the following limit:
limx0ax+x cos xb sin x

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Solution

Here limx0ax+x cos xb sin x[00 form]

limx0ax+x cos xb sin x=[axb sin x+x cos xb sin x]

= limx0[ab×1sin xx+1b sin xx cos x]

= limx0[ab×1sin xx+1b tan xx]

= ab+1b=a+1b.


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