lim x tends to 1

{1/( x2+x-2) - x/ (x3-1)} is evaluated to be

a)1/9

b)9

c)-1/9

d) none of these

limx1 1x2+x-2-xx3-1Now 1x2+x-2-xx3-1= 1x2+2x-x-2-xx-1x2+x+1 =1x+2x-1-xx-1x2+x+1 =1x-11x+2-xx2+x+1 =1x-1x2+x+1-x2-2xx+2x2+x+1 =1x-11-xx+2x2+x+1=-1x+2x2+x+1Now putting this we get, limx1 1x2+x-2-xx3-1=limx1-1x+2x2+x+1=-11+21+1+1=-19

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1/(x2+x-2)=1/{(x-1)(x+2)}

1/(x-1) {1/(x+2) - x/(x2+1+x)}

1/(x-1){(1-x) / (x+2)(x2+x+1)}

-1 /(x+2)(x2+x+1))

putting limits

-1/9

  • 3
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