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Could you please calculate this limit `lim(x-> oo) (4x+7)/(x + sqrt x)`

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thezy | eNoter

Posted September 7, 2013 at 1:53 PM via web

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Could you please calculate this limit `lim(x-> oo) (4x+7)/(x + sqrt x)`

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted September 7, 2013 at 2:08 PM (Answer #1)

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The limit `lim(x-> oo) (4x+7)/(x + sqrt x)` has to be determined.

`lim(x-> oo) (4x+7)/(x + sqrt x)`

substituting `x = oo` , gives the indeterminate form `oo/oo` . Use l'Hopital's rule and replace the numerator and denominator with their derivative.

= `lim_(x->oo) 4/(1 + (1/(2*sqrt x)))`

As `x -> oo` , `1/x -> 0`

Substituting `x = oo`

= 4

The limit `lim(x-> oo) (4x+7)/(x + sqrt x) = 4`

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