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lim ( x to 0) ((2 ^(x) + 3 ^(x) + 6 ^(x)...

`lim _( x to 0) ((2 ^(x) + 3 ^(x) + 6 ^(x))/(3))^(3//x)` [is equal to `"_____."`

Text Solution

Verified by Experts

The correct Answer is:
36
Given limit is of the from `(1) ^(oo)`
`L =e ^(lim _(x to 0)(2 ^(x) log 2 + 3 ^(x) log 3 +6 ^(x) log 6)/(1))`
`L =e ^(log (2xx3xx6))=e ^(log 36)=36`
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