CBSE Class 11-science Answered

$I f space limit as x rightwards arrow 1 of fraction numerator x to the power of begin display style 1 over 100 end style end exponent minus 1 over denominator x to the power of k minus 1 end fraction equals 5 space t h e n space f i n d space t h e space v a l u e space o f space k ?$ Please provide solution to this question

Asked by Topperlearning User | 16 Nov, 2016, 01:54: AM

Expert Answer

$limit as x rightwards arrow 1 of fraction numerator x to the power of begin display style 1 over 100 end style end exponent minus 1 over denominator x to the power of k minus 1 end fraction equals limit as x rightwards arrow 1 of fraction numerator begin display style fraction numerator x to the power of 1 over 100 end exponent minus 1 over denominator x minus 1 end fraction end style over denominator begin display style fraction numerator x to the power of k minus 1 over denominator x minus 1 end fraction end style end fraction U sin g space t h e space p r o p e r t y space limit as x rightwards arrow a of fraction numerator x to the power of n minus a to the power of n over denominator x minus a end fraction equals n a to the power of n minus 1 end exponent space w e space c a n space w r i t e limit as x rightwards arrow 1 of fraction numerator begin display style fraction numerator x to the power of 1 over 100 end exponent minus 1 over denominator x minus 1 end fraction end style over denominator begin display style fraction numerator x to the power of k minus 1 over denominator x minus 1 end fraction end style end fraction equals fraction numerator begin display style 1 over 100 end style 1 to the power of begin display style fraction numerator negative 99 over denominator 100 end fraction end style end exponent over denominator k 1 to the power of k minus 1 end exponent end fraction equals fraction numerator 1 over denominator 100 k end fraction G i v e n space t h a t space limit as x rightwards arrow 1 of fraction numerator x to the power of begin display style 1 over 100 end style end exponent minus 1 over denominator x to the power of k minus 1 end fraction equals 5 rightwards double arrow fraction numerator 1 over denominator 100 k end fraction equals 5 rightwards double arrow k equals 1 over 500$