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Evaluate lim(xtosqrt(10)) (sqrt(7+2x)-(s...

Evaluate `lim_(xtosqrt(10)) (sqrt(7+2x)-(sqrt(5)+sqrt(2)))/(x^(2)-10).`

Text Solution

Verified by Experts

The correct Answer is:
`(1)/(2sqrt(10)"("sqrt(5)+sqrt(2)")")`
Rationalizing Nr., we get
`=underset(xtosqrt(10))lim(7+2x-(sqrt(5)+sqrt(2))^(2))/(x^(2)-10).(1)/(sqrt(7+2x)+(sqrt(5)+sqrt(2)))`
`= (1)/(sqrt(7+2sqrt(5))+(sqrt(5)+sqrt(2)))underset(xtosqrt(10))lim(2(x-sqrt(10)))/((x-sqrt(10))(x+sqrt(10)))`
`= (1)/((sqrt(5)+sqrt(2))+(sqrt(5)+sqrt(2))).(1)/(sqrt(10))`
`=(1)/(2sqrt(10)(sqrt(5)+sqrt(2)))`
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