My answer was wrong. I started the problem off by conjugate rule, but i think i mesed up somewhere with the lone values near the radical roots. And i was plugging in 0 at the end. Maybe that was wrong.

Veteran
Apr 14, 2017

#1**+2 **

Find the following limit:

lim_(x->0) (sqrt(4 x + 16) - 4)/(7 x)

(sqrt(4 x + 16) - 4)/(7 x) = (sqrt(4 x + 16) - 4)/(7 x):

lim_(x->0) (sqrt(4 x + 16) - 4)/(7 x)

lim_(x->0) (sqrt(4 x + 16) - 4)/(7 x) = 1/7 (lim_(x->0) (sqrt(4 x + 16) - 4)/x):

1/7 lim_(x->0) (sqrt(4 x + 16) - 4)/x

(sqrt(4 x + 16) - 4)/x = ((sqrt(4 x + 16) - 4) (4 + sqrt(4 x + 16)))/(x (4 + sqrt(4 x + 16))) = 4/(4 + sqrt(4 x + 16)):

(lim_(x->0) 4/(4 + sqrt(4 x + 16)))/(7)

lim_(x->0) 4/(4 + sqrt(4 x + 16)) = 4/(4 + sqrt(16 + 4 0)) = 1/2:

1/71/2

1/(2 7) = 1/14:

**Answer: | 1/14**

Guest Apr 14, 2017