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Find the value of lim(xto0^(+)) (3(log(e...

Find the value of `lim_(xto0^(+)) (3(log_(e)x)^(2)+5log_(e)x+6)/(1+(log_(e)x)^(2)).`

Text Solution

Verified by Experts

We known that `underset(xto0^(+))limlog_(e)x=-oo`
`:." "underset(xtoo^(+))lim(3(log_(x)x)^(2)+5log_(e)x+6)/(1+(log_(e)x)^(2))" "((oo)/(oo)"from")`
`=underset(xto0^(+))lim((3+(5)/((log_(x)x))+(6)/((log_(e)x)^(2)))/(1+(1)/(log_(e)x)^(2)))`
`=3`
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