1.

Evaluate the following lim_(xto3)(x^2+2x-15)/(x^2-x-6)

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SOLUTION :`lim_(xto3)(X^2+2x-15)/(x^2-x-6)`
`=lim_(xto3)(x^2+5x-3x-15)/(x^2-3x+2x-6)`
`=lim_(xto3)(x(x+5)-3(x-5))/(x(x-3)+2(x-3))`
`=lim_(xto3)((x-3)(x+5))/((x-3)(x+2))`
`=lim_(xto3)(x+5)/(x+2)=(3+5)/(3+2)=8/5`


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