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Evaluate lim(xto2) (x^(2)-5x+6)/(x^(2)-4...

Evaluate `lim_(xto2) (x^(2)-5x+6)/(x^(2)-4).`

Text Solution

Verified by Experts

When`x=2,` the expression `(x^(2)-5x+6)/(x^(2)-4)` assumes the indeterminate form `0/0.` Here, (x-2) is a common factor in numerator and denominator. Factorizing the numerator and denominator, we have
`underset(xto2)lim(x^(2)-5x+6)/(x^(2)-4)=underset(xto2)lim((x-2)(x-3))/((x+2)(x-2))`
`=underset(xto2)lim(x-3)/(x+2)=(2-3)/(2+2)=-(1)/(4)`
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