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Evaluate the limit: lim(x->a)(sqrt(3x-a)...

Evaluate the limit: `lim_(x->a)(sqrt(3x-a)-sqrt(x+a))/(x-a)`

Text Solution

Verified by Experts

The correct Answer is:
`1//sqrt(2a)`
`underset(xtoa)lim(sqrt(3x-a)-sqrt(x+a))/(x-a)`
`=underset(xtoa)lim(sqrt(3x-a)-sqrt(x+a))/((x-a))xx(sqrt(3x-a)+sqrt(x+a))/(sqrt(3x-a)+sqrt(x+a))`
`=underset(xtoa)lim((3x-a)-(x+a))/((x-a)(sqrt(3x-a)+sqrt(x+a)))`
=(2)/(2sqrt(2a))=(1)/(sqrt(2a))`
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