Evaluate the limit: `lim_{u->3}sqrt{u^2+3u+5}` 

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lfryerda eNotes educator| Certified Educator

When evaluating limits, try direct substitution first, then if necessary, move on to factoring, rationalization or one-sided limits.  In this case, direct substitution will work:

`lim_{u->3}sqrt{u^2+3u+5}`   replace each u value with 3

`=sqrt{3^2+3(3)+5}`

`=sqrt{9+9+5}`

`=sqrt23`

The limit evaluates to `sqrt23` .