Maharashtra State BoardHSC Commerce 11th
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Evaluate the following Limits: limx→0[log100+log(0.01+x)x] - Mathematics and Statistics

Sum

Evaluate the following Limits: `lim_(x -> 0)[(log 100 + log (0.01 + x))/x]`

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Solution

`lim_(x -> 0)[(log 100 + log (0.01 + x))/x]`

= `lim_(x -> 0) log[100 (0.01 + x)]/x`

= `lim_(x -> 0) (log(1 + 100x))/x`

= `lim_(x -> 0)[(log(1 + 100x))/(100x)] xx 100`

= 1 x 100    ...`[("As"  x -> 0","  100  x -> 0 and ),(lim_(x -> 0) (log(1 + x))/x = 1)]` 

= 100

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APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board
Chapter 7 Limits
Miscellaneous Exercise 7 | Q II. (17) | Page 106
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