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Pllllllzzzzzzzzzzzxxxxzzzzzzzzzzzzzzz. ..reply wid proper explanation....

Pllllllzzzzzzzzzzzxxxxzzzzzzzzzzzzzzz. ..reply wid proper explanation.... 

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Grade:11

1 Answers

Aditya Gupta
2080 Points
2 years ago
hello jahnvi this is an easy ques.
write it as [p(1 – x^q) – q(1 – x^p)]/[(1 – x^p)(1 – x^q)]
now note that the denominator has become (1 – x^p)(1 – x^q).
we can write this as [(1 – x^p)/(1 – x)]*[(1 – x^q)/(1 – x)]*(1 – x)^2
now as x tends to 1, (1 – x^p)/(1 – x) tends to p and (1 – x^q)/(1 – x) tends to q (because lim x^n – a^n/x – a is na^n-1)
so we are left with the limit:
(1/pq)*lim [p(1 – x^q) – q(1 – x^p)]/(1 – x)^2
now you can easily apply l’hospital rule twice to obtain the answer as (p – q)/2

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