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