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)
4 answers
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
(6-17/e^x)/3 , as x ----> ∞ , the expression ---> 2
and 2√x/√(x-1) ----> 2 , as x ---->∞
so as x---->∞
2 < f(x) < 2
which implies f(x) = 2
divide top and bottom by e^x
we get
(6-17/e^x)/3 , as x ----> ∞ , the expression ---> 2
and 2√x/√(x-1) ----> 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, i just want to make sure i fully understand this. thank you so much! you are a life saver!
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, i just want to make sure i fully understand this. thank you so much! you are a life saver!
in (6-17/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 (6-0)/3 = 2
for the right side 2√x/√(x-1)
when x is really really large, do you think it makes any difference if we take √x or √(x-1) ?
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
what happens when you divide 17 by a very very very large number ?
Doesn't it go to zero ?
so you have (6-0)/3 = 2
for the right side 2√x/√(x-1)
when x is really really large, do you think it makes any difference if we take √x or √(x-1) ?
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
1 answer