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Evalvate lim(xrarr0)((3^(x)-2^(x))/(x))....

Evalvate `lim_(xrarr0)((3^(x)-2^(x))/(x)).`

Text Solution

Verified by Experts

`lim_(xto0)((3^(x)-2^(x))/(x))=lim_(xto0){((3^(x)-1)-(2^(x)-1))/x}`
`=lim_(xto0)((3^(x)-1)/(x))-lim_(xto0)((2^(x)-1)/(x))`
`(log3-log2)=log""(3)/(2)" "[becauselim_(xto0)((a^(x)-1)/(x))=loga].`
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