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## [STPM] Maths T needs help!! mitsukolyn Member   Join Date: Sep 2007 Posts: 341 #1 20-06-2008 [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]  ken_cck_kid Super Junior Member   Join Date: Jun 2008 Posts: 30 #2 20-06-2008 just wanna help.. e^x - 3e^-x ? 2 e^x << 2 + 3e^-x e^2x << 2e^x + 3 ( multiply by e^x) e^2x-2e^x-3<<0 (a quadratic equation) (e^x-3)(e^x+1) <<0 try to continue ya, tis should be the way la if i'm not mistaken..haha..  luke KittyLover Administrator   Join Date: Nov 2003 Posts: 1,878 #3 21-06-2008 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 __________________   Member
#4 22-06-2008 reply

Quote:
 Originally Posted by luke 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
haha..im stuck in the half way thts y i turn to here...wow...ur so smart!!! but cn i knw wad's ln means and when to use it??  chiunlin Slightly Senior Member   Join Date: Jan 2004 Posts: 705 #5 22-06-2008 ln = log to the base e/natural log __________________ 知不知道饮酒和饮水有什么区别？酒越饮越暖，水越喝越寒。 你越想忘记一个人时，其实你越会记得他。人的烦恼就是记性太好，如果可以把所有事都忘掉，以后每一日都是个 新开始，你说多好  The Following User Says Thank You to chiunlin For This Useful Post:
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#6 26-06-2008 Quote:
 Originally Posted by chiunlin ln = log to the base e/natural log
thanks!! i got it d...   lonewolf5999 Super Junior Member   Join Date: Jul 2008 Posts: 44 #7 19-07-2008 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 29-07-2008 luke is still da smart ass.

Quote:
 Originally Posted by luke 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  Lance2 Super Junior Member   Join Date: Feb 2010 Posts: 1 #9 21-02-2010 Re: [STPM] Maths T needs help!! Nice post, Keep up the good work man. __________________ jewelry designs and handbag reviews and digital camera models  smallkid Super Junior Member   Join Date: Feb 2010 Posts: 12 #10 11-03-2010 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; 11-03-2010 at 07:34 PM. Reason: Automerged Doublepost   Tags mathematics, stpm Thread Tools Show Printable Version Email this Page Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is Off Similar Threads Thread Thread Starter Forum Replies Last Post infested_ysy Education 5 16-06-2009 08:48 PM UlquiorraSchiffer SPM & STPM 0 09-09-2007 09:46 AM qfeng Education 9 20-01-2007 09:21 AM lolilo Education 37 05-06-2005 04:45 AM joebf86 Education 4 15-09-2004 07:04 AM

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