Limits and Derivatives

Limits and Derivatives

Question

Evaluate space space space space space limit as straight x rightwards arrow 0 of fraction numerator sin space ax over denominator bx end fraction.

Answer
space space space space space space space space space space limit as straight x rightwards arrow 0 of fraction numerator sin space ax over denominator bx end fraction equals 1 over straight b limit as straight x rightwards arrow 0 of fraction numerator sin space ax over denominator ax end fraction xa equals straight a over straight b semicolon fraction numerator sin space ax over denominator ax end fraction                                   [∵ xrightwards arrow0rightwards double arrowaxrightwards arrow0]

   space space space space space space space space space space space space space space equals straight a over straight b.1 equals straight a over straight b

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