+280 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.
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
