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Evaluate the following Limits: limx→0(1+x5)1x - Mathematics and Statistics

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Question

Evaluate the following Limits: `lim_(x -> 0)(1 + x/5)^(1/x)`

Sum

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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Limits of Exponential and Logarithmic Functions
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Chapter 7: Limits - MISCELLANEOUS EXERCISE - 7 [Page 106]

APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) [English] 11 Standard Maharashtra State Board
Chapter 7 Limits
MISCELLANEOUS EXERCISE - 7 | Q II. 8) | Page 106
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