Question #24625

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Answer 1 · 2017-04-05T10:21:36

$0 .$ $0.$

Let $x=1/y. :. x to -oo rArr y to 0.$

$:." The Reqd. Lim.="lim_(y to 0){-5/y^2+6/y+3}/sqrt{(1/y^4+1/y)^2+1},$

$=lim_(y to 0){1/y^2(-5+6y+3y^2)}/sqrt{(1+y^3)^2/y^8+1},$

$=lim_(y to 0){1/y^2(-5+6y+3y^2)}/sqrt{((1+y^3)^2+y^8)/y^8},$

$=lim_(y to 0)(1/y^2-:1/y^4)(-5+6y+3y^2)/sqrt((1+y^3)^2+y^8),$

$=lim_(y to 0) (y^2(-5+6y+3y^2))/sqrt((1+y^3)^2+y^8),$

$=(0(-5+0+0))/sqrt((1+0)^2+0),$

$=0.$

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