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CBSE Class 11-science Answered

Asked by Topperlearning User | 10 Nov, 2016, 12:31: AM
answered-by-expert Expert Answer

limit as x rightwards arrow a of fraction numerator x to the power of begin display style 3 over 5 end style end exponent minus a to the power of 3 over 5 end exponent over denominator x to the power of begin display style 1 third end style end exponent minus a to the power of begin display style 1 third end style end exponent end fraction
equals limit as x rightwards arrow a of fraction numerator begin display style fraction numerator x to the power of 3 over 5 end exponent minus a to the power of 3 over 5 end exponent over denominator x minus a end fraction end style over denominator begin display style fraction numerator x to the power of 1 third end exponent minus a to the power of 1 third end exponent over denominator x minus a end fraction end style end fraction
U sin g space t h e space r e s u l t colon 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 a of fraction numerator begin display style fraction numerator x to the power of 3 over 5 end exponent minus a to the power of 3 over 5 end exponent over denominator x minus a end fraction end style over denominator begin display style fraction numerator x to the power of 1 third end exponent minus a to the power of 1 third end exponent over denominator x minus a end fraction end style end fraction equals fraction numerator begin display style limit as x rightwards arrow a of fraction numerator x to the power of 3 over 5 end exponent minus a to the power of 3 over 5 end exponent over denominator x minus a end fraction end style over denominator begin display style limit as x rightwards arrow a of fraction numerator x to the power of 1 third end exponent minus a to the power of 1 third end exponent over denominator x minus a end fraction end style end fraction equals fraction numerator begin display style 3 over 5 end style a to the power of negative begin display style 2 over 5 end style end exponent over denominator begin display style 1 third end style a to the power of negative begin display style 2 over 3 end style end exponent end fraction equals 9 over 5 a to the power of 4 over 15 end exponent

Answered by | 10 Nov, 2016, 02:31: AM
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