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प्रश्न
Evaluate the following limits: `lim_(y -> 2) [(2 - y)/(sqrt(3 - y) - 1)]`
उत्तर
`lim_(y -> 2) [(2 - y)/(sqrt(3 - y) - 1)]`
= `lim_(y -> 2)[(2 - y)/(sqrt(3 - y) - 1) xx (sqrt(3 - y) + 1)/(sqrt(3 - y) + 1)]`
= `lim_(y -> 2) ((2 - y)(sqrt(3 - y) + 1))/(3 - y - 1)`
= `lim_(y -> 2) ((2 - y)(sqrt(3 - y) + 1))/(2 - y)`
= `lim_(y -> 2) (sqrt(3 - y) + 1) ...[("As" y -> 2"," y ≠ 2),(therefore y - 2 ≠ 0 therefore 2 - y ≠0)]`
= `sqrt(3 - 2) + 1`
= 1 + 1
= 2
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