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#1
20062008
[STPM] Maths T needs help!!
I need help on this question...
Question: Find the set of values of x for the following inequalities. b)e^x  3e^x ? 2 [hint: multiply both sides by e^x] 
Super Junior Member

#2
20062008
just wanna help..
e^x  3e^x ? 2
e^x << 2 + 3e^x e^2x << 2e^x + 3 ( multiply by e^x) e^2x2e^x3<<0 (a quadratic equation) (e^x3)(e^x+1) <<0 try to continue ya, tis should be the way la if i'm not mistaken..haha.. 
KittyLover
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#3
21062008
e^x  3e^(x) < 2
e^(2x)  3 < 2e^x e^(2x)  2e^x  3 < 0 let Z = e^x, therefore: Z^2  2Z  3 < 0 (voila! normal quadratic inequality!) after a bit of drawing the curve we figure out that, 1 < Z < 3 substitute back, 1 < e^x < 3 but e^x cannot be less than 0, thus 0 =< e^x < 3 ln 0 =< ln (e^x) < ln 3 negative infinity =< x < ln 3 simply means x < ln 3
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Member

#4
22062008
reply
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Slightly Senior Member

#5
22062008
ln = log to the base e/natural log
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#6
26062008

Super Junior Member

#7
19072008
As in the hint, multiply both sides to obtain
e^2x  3 < 2e^x use the substitution u = e^x to get u^2 3 < 2u, which is easily solved substitute back e^x, but note that e^x is always positive, so you will need to reject any answers contradicting this fact. 
Less Junior Member

#8
29072008
luke is still da smart ass.
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Super Junior Member

#9
21022010
Re: [STPM] Maths T needs help!!
Nice post, Keep up the good work man.

Super Junior Member

#10
11032010
Re: [STPM] Maths T needs help!!
I found this question in fajar bakti ace ahead (volume 2)
Exam practise chapter 8 Q21. Suppose the time T taken for a car wash is normally distributed with mean 6minutes and standard deviation 1.5 minutes. c) If 1000 cars are washed, what is the probability that not more than one car takes more than 10.62 minutes. Answer : 0.3399 Anyone knows how to do it? I've tried poisson approximation, but i'm still no where near the solution Last edited by smallkid; 11032010 at 07:34 PM. Reason: Automerged Doublepost 
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