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Evaluate: ("lim")(xvec2)(x^2-x-2)/(x^2-2...

Evaluate: `("lim")_(xvec2)(x^2-x-2)/(x^2-2x-"sin"(x-2))`

Text Solution

Verified by Experts

`underset(xto2)lim(x^(2)-x-2)/(x^(2)-2x-sin(x-2))" "`(0/0 from)
`=underset(xto2)lim((x-2)(x+1))/((x-2)-sin(x-2))`
`=underset(xto2)lim(x+1)/(x-(sin(x-2))/(x-2))`
`(2+1)/(2-1)=3`
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