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Evaluate the following limits : Lim(x t...

Evaluate the following limits :
`Lim_(x to oo) (sqrt(3x^(2)-1)-sqrt(2x^(2)-1))/(4x+3)`

Text Solution

Verified by Experts

Dividing each term in the numerator and denominator by x, we get
`underset(xtooo)lim(sqrt(3x^(2)-1)-sqrt(2x^(2)-1))/(4x+3)`
`=underset(xtooo)lim(sqrt(3-1//x^(2))-sqrt(2-1//x^(2)))/(4+3//x)`
`=(sqrt(3)-sqrt(2))/(4)`
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