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Question
Evaluate `lim_(x -> 0) (sqrt(2 + x) - sqrt(2))/x`
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Solution
Put y = 2 + x
So that when x → 0, y → 2.
Then `lim_(x -> 0) (sqrt(2 + x) - sqrt(2))/x`
= `lim_(y -> 2) (y^(1/2) - 2^(1/2))/(y - 2)`
= `1/2(2)^(1/2 - 1)`
= `1/2 * 2^(-1/2)`
= `1/(2sqrt(2))`
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