Find the limit: `lim_(x->16) (16-x)/(sqrtx-4)` `` ` `

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hala718 eNotes educator| Certified Educator

`lim_(x->16) (16-x)/(sqrtx - 4)`

First we plug in x= 16 ==> lim = 0/0

Then, we know that 16 is the root for both numerator and denominator.

Therefore, we will need to factor and reduce common factor between numerator and denominator.

`==> lim_(x->16) (16-x)/(sqrtx-4) = lim_(x->16) ((4-sqrtx)(4+sqrtx))/(sqrtx-4)`

`= lim_(x->16) (-(4+sqrtx)) = lim_(x->16) (-4-sqrtx)`

` = -4-sqrt16= -4-4= -8`

`==> lim_(x->16) (16-x)/(sqrtx-4)= -8`

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