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Evaluate lim(x to 0) ((x+4)/(2-x))^((x^(...

Evaluate `lim_(x to 0) ((x+4)/(2-x))^((x^(2)+2x-3)/(x-1))`

Text Solution

Verified by Experts

`underset(xto0)lim((x+4)/(2-x))^((x^(2)+2x-3)/(x-1))`
`=(underset(xto0)lim(x+4)/(2-x))^((x^(2)+2x-3)/(x-1))`
`((0+4)/(2-0))^((0+0-3)/(0-1))`
`2^(-3)`
`1//8`
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