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Evaluate: ("lim")(xvec0)((729)^x-(243)^x...

Evaluate: `("lim")_(xvec0)((729)^x-(243)^x-(811)^x+9^x+3^x-1)/(x^3)`

Text Solution

Verified by Experts

The correct Answer is:
`6(ln3)^(3)`
`L=underset(xto0)lim((729)^(x)-(243)^(x)-(81)^(x)+9^(x)+3^(x)-1)/(x^(3))`
`=underset(xto0)lim((3^(x)-1))/(x)xx((9^(x)-1))/(x)xx((27^(x)-1))/(x)`
`=("1n "3)("1n "9)("1n "27)`
`=6("1n "3)^(3)`
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