calculus
posted by maura (urgent!!) on .
Can someone please help me with these two? im so lost and i really appreciate it if someone could show me what to do!
1) To evaluate
lim x→infinity sqrt (x^2 + 4)
first consider that as x becomes infinitely large, x^2+4 > _____
2)Find lim x→ infinity f(x)if,
for all x > 1,
(6e^x − 17)/3e^x < f(x) < 2sqrt(x)/ sqrt (x − 1)

forget the first one i got it. just the second one i don't know where to begin

for (6e^x  17)/(3e^x)
divide top and bottom by e^x
we get
(617/e^x)/3 , as x > ∞ , the expression > 2
and 2√x/√(x1) > 2 , as x >∞
so as x>∞
2 < f(x) < 2
which implies f(x) = 2 
SOOOO HAPPY YOU ANSWERED ME!
ok now im just trying to process this in my head. i understand dividing it by e^x but you lost me at the expression >2
sorry to be a pain in the ass, i just want to make sure i fully understand this. thank you so much! you are a life saver! 
in (617/e^x)/3 , as x > ∞
what happens when you divide 17 by a very very very large number ?
Doesn't it go to zero ?
so you have (60)/3 = 2
for the right side 2√x/√(x1)
when x is really really large, do you think it makes any difference if we take √x or √(x1) ?
e.g. take
√123456789 and √123456788
now divide them to get 1.000000004
so the right side would be 2.00000008 or just plain 2
so the f(x) is sandwiched between 2 and 2 , thus it MUST BE 2