I\'m only able to see the answer to a) to someone else\'s previous question belo
ID: 2893044 • Letter: I
Question
I'm only able to see the answer to a) to someone else's previous question below. Were the solutions to b), c), and d) also posted? Thanks!
a) Put f[x] = (2 x^4 + 50 Log[x])/(x^4 + 3 x^2 + 1) . What do you say is the limiting value Underscript[lim, x -> Infinity] f[x] ? b) What do you say is the limiting value Underscript[lim, x -> Infinity](x^0.8 + 4 Log[x])/(3 x^0.8 + 2 Log[x]) ? Illustrate with a plot. c) What do you say is the limiting value Underscript[lim, x -> Infinity](45 x^8 - 123 Cos[x] + 6 x^6)/e^(0.04 x) Illustrate with a plot. d) What do you say is the limiting value Underscript[lim, x -> Infinity]Log[x]/x^0.03 ? Illustrate with a plot. e) Rank the following functions in order of dominance as x Infinity : x^52 , 0.0004 e^(0.01 x) , e^(0.02 x)/x , x Log[x] , 89 x^2 , Sqrt[x] , 100 Log[x] , 17 x , 0.08 x^3 , 1.3 ^-6 e^(2 x) , 100 x^0.004 .
Explanation / Answer
a)
We have numerator leading term to be 2x^4
Denominator leading term to be x^4
So, to find infinite limit, we simply divide these leading terms because the degrees of numerator and denominator are the same
2/1, i.e 2
So, answer = 2
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b)
Same thing on the next one
Itll be 1/3
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c)
45x^8 and e^(0.04x) are the dominant terms
Clearly 45x^8 grows lightning fast compared to e^(0.04x)
So, when we divide. the limit becomes
(very very very large number) / (large number),
i.e
+infinity
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d)
lnx grows faster
So, +infinity again
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