I have to compute this limit: \(\displaystyle\lim_{{{x}\to\infty}}{3}{\left(\sqrt{{{x}}}\sqrt{{{x}-{3}}}-{x}+{2}\right)}\)

Guadalupe Glass 2022-03-31 Answered
I have to compute this limit:
limx3(xx3x+2)
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Answers (2)

Luciana Cline
Answered 2022-04-01 Author has 14 answers
The two standard techniques work: multiply and divide by the conjugate, then divide both numerator and denominator by the highest power of x
limx3(xx3x+2)=3limx(x23x(x2))
=3limx(x23x(x2))(x23x+(x2))x23x+(x2)
=3limx(x23x)(x2)2x23x+(x2)
=3limxx23xx2+4x4x23x+(x2)
=3limxx4x23x+(x2)
=3limx1x(x4)1x(x23x+(x2))
=3limx14x13x+12x}
=3(11+1)=32
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Jeffrey Jordon
Answered 2022-07-05 Author has 2313 answers

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