E v a l u a t e space limit as x rightwards arrow 0 of fraction numerator sin to the power of k squared minus 2 k plus 1 end exponent x over denominator x end fraction equals 1 space f i n d space t h e space v a l u e space o f space k ?

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Asked by Topperlearning User | 16th Nov, 2016, 02:27: AM

Expert Answer:

limit as x rightwards arrow 0 of fraction numerator sin to the power of k squared minus 2 k plus 1 end exponent x over denominator x end fraction equals 1
w e space k n o w space t h a t space limit as x rightwards arrow 0 of fraction numerator sin x over denominator x end fraction equals 1
O n space c o m p a r i n g space t h e space p o w e r s space o f space sin x space w e space g e t
k squared minus 2 k plus 1 equals 1
rightwards double arrow k squared minus 2 k equals 0
rightwards double arrow k equals 0 comma 2

Answered by  | 16th Nov, 2016, 04:27: AM

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