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Evaluate lim(xtoa) ((2+x)^(5//2)-(a+2)^(...

Evaluate `lim_(xtoa) ((2+x)^(5//2)-(a+2)^(5//2))/(x-a)`

Text Solution

Verified by Experts

Given, `underset(xtoa)"lim"((2+x)^(5//2)-(a+2)^(5//2))/(x-a) = underset(xtoa)"lim"((2+x)^(5//2)-(a+2)^(5//2))/((2+x)-(a+2))`
`=5/2(a+2)^(5/2-1)` `[therefore underset(xtoa)"lim"(x^(n)-a^(n))/(x-a)=na^(n-1)]`
`=5/2(a+2)^(3//2)` `[therefore a to a rArr x+2 to a+2]`
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