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

Guadalupe Glass

Guadalupe Glass

Answered question

2022-03-31

I have to compute this limit:
limx3(xx3x+2)

Answer & Explanation

Luciana Cline

Luciana Cline

Beginner2022-04-01Added 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
Jeffrey Jordon

Jeffrey Jordon

Expert2022-07-05Added 2605 answers

Answer is given below (on video)

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