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Use the formula lim(x to 0 ) (a^(x) - ...

Use the formula ` lim_(x to 0 ) (a^(x) - 1) / x log_(e) a`, to find ` lim_( x to 0) (2^(x)-1)/((1+x)^(1//2) - 1) `.

Text Solution

Verified by Experts

The correct Answer is:
`log_(e)4`
`underset( x to 0) lim (2^(x) - 1)/(sqrt(1+x)-1 ) xx(sqrt(1+x)+1)/(sqrt(1+x)+1) = underset(x to 0)lim ((2^(x)-1)(sqrt(1+x)+1))/x `
` = log_(e) (2)*(2)`
` = 2 log_(e) 2 = log_(e) 4`
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