Question

Evaluate the following limits: `lim_(y -> 2) [(2 - y)/(sqrt(3 - y) - 1)]`

Answer 1

`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