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Question
Evaluate the following Limits: `lim_(x -> 0)(1 + x/5)^(1/x)`
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Solution
`lim_(x -> 0)(1 + x/5)^(1/x)`
= `lim_(x -> 0)[(1 + x/5)^(5/x)]^(1/5)`
= `"e"^(1/5) ...[lim_(x -> 0) (1 + x)^(1/x) = "e"]`
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\[\lim_{x\to0}\frac{\mathrm{e}^{\tan x}-\mathrm{e}^{x}}{\tan x-x}=\]
