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Match the following lists (where [x] rep...

Match the following lists (where `[x]` represents the greatest integer function) and then choose the correct code.

Codes :
`{:(,"a b c d"),((1),"s r q p"),((2),"q p s p"),((3), "s r p q"),((4),"p p q r"):}`

Text Solution

Verified by Experts

The correct Answer is:
`(2)`
a. `underset(xto0)lims(-1)^([1//x])`
`L.H.L.=underset(hto0)lim(0-h)(-1)^([(1)/(0-h)])=0`
`R.H.L.=underset(hto0)lim(0+h)(-1)^([(1)/(0+h)])=0`
b. `underset(xto2)lim(-1)^([x])`
`L.H.L.=underset(hto0)lim(-1)^([2-h])=(-1)^(1)=-1`
`R.H.L.=underset(hto0)lim(-1)^([2+h])=(-1)^(2)=1`
So limit does not exist.
c.`underset(xto(3)/(2))lim(x-[x])`
`L.H.L.=underset(hto0)lim(3)/(2)-h-[(3)/(2)-h]=underset(hto0)lim(3)/(2)-h-1=(1)/(2)`
`R.H.L.=underset(hto0)lim(3)/(2)+h-[(3)/(2)+h]=underset(hto0)lim(3)/(2)+h-1=(1)/(2)`
`L.H.L.=R.H.L.=(1)/(2)`
`underset(xto0)lim[x]((e^(1//x)-1)/(e^(1//x)+1))`
`L.H.L.=underset(hto0)lim[0-h](((1)/(e^(0-h)-1))/((1)/(e^(0-h)+1)))`
`=underset(hto0)lim[-h]((e^(-(1)/(h))-1)/((1)/(e^(0-h)+1)))=(-1)xx(-1)=1`
R.H.L.`=underset(hto0)lim[0+h]((e^((1)/(h))-1)/(e^((1)/(h)+1)))=0`
Limit does not exist
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