Q9 (c) (iii) (1 Viewer)

[xeriphic]

have no idea what this question was about, what do we deduce from

 

[~*HSC 4 life*~]

i left this blank too!

i wrote some stuff but gonowhere

 

[xeriphic]

lol yer I tried to related to the previous question but nothing came out

 

[Jezzabelle]

yeh.. i only had 15 min left on the clock and hadnt done 10 yet.. which from reading time i worked out i could attempt.. so scribbled some bs for 9 c and went on to solve most of 10

 

[Sweet_Lemon]

substitute numbers in...probably wrong anyway~~

 

[Managore]

I just stated x=e was maximum, and in the equation was true, and that x=2 and x=3 also gave true answers, thus x^e>_e^x (or whatever)

 

[acmilan]

the max value given when x = e is f(x) = 1/e

so that means f(x) <= 1/e

(ln x)/x <= 1/e
elnx <= x
ln (x^e) <= x
x^e <= e^x

hence e^x >= x^e

 

[Sweet_Lemon]

I just stated x=e was maximum, and in the equation was true, and that x=2 and x=3 also gave true answers, thus x^e>_e^x (or whatever)

i sub tat e first...then the x=2....then going back to x=1~~ since it says x>0

 

[Sweet_Lemon]

the max value given when x = e is f(x) = 1/e

so that means f(x) <= 1/e

(ln x)/x <= 1/e
elnx <= x
ln (x^e) <= x
x^e <= e^x

hence e^x >= x^e

ya answer is perhaps d most correct~~ dam i stuffed it!!

 

[hiphophorray123]

uhh max value means a max stat point doenst it?

i did all that dy/dx crap

 

[angelduck]

sames, worked out pretty well~!

 

[~ ReNcH ~]

For that question, I kind of fudged it:
I said:

Since 1/e is a local max:
1/e <= lnx/x
.'. 1 <= elnx/x
.'. x <= elnx
.'. x <= ln(x^e)
.'. e^x >= x^e for x>0

acmilan....is this right, coz I pretty much fudged it??

 

[JimBob]

I had no idea, so I wrote:
x^e<=e^x for x=e
x^x<=x^x
e^e<=e^e
Therefore, x^e<=e^x

It was an attempt at getting at least one mark...

 

[speersy]

the max value given when x = e is f(x) = 1/e

so that means f(x) <= 1/e

(ln x)/x <= 1/e
elnx <= x
ln (x^e) <= x
x^e <= e^x

hence e^x >= x^e

ohh hell yeah thats what i did, after much working out than finally stumbling on the answer.
I was just reading this thing that said
"Practise writing neatly and fluently. it is not too late to improve the way your work reads. (Remember that marks may be deducted for careless or badly arranged work.) The examiners mark quickly, and it is to your advantage to communicate well"

Is this true, even though the question is eventually correct, they may subtract marks?

 

[acmilan]

ohh hell yeah thats what i did, after much working out than finally stumbling on the answer.
I was just reading this thing that said
"Practise writing neatly and fluently. it is not too late to improve the way your work reads. (Remember that marks may be deducted for careless or badly arranged work.) The examiners mark quickly, and it is to your advantage to communicate well"

Is this true, even though the question is eventually correct, they may subtract marks?

I cant see them taking a mark away if you get the right answer no matter how long the method (unless you contradict yourself somewhere)

For that question, I kind of fudged it:
I said:

Since 1/e is a local max:
1/e <= lnx/x
.'. 1 <= elnx/x
.'. x <= elnx
.'. x <= ln(x^e)
.'. e^x >= x^e for x>0

acmilan....is this right, coz I pretty much fudged it??

Its basically the same thing

 

[garry]

wouldn't it be easier to draw a graph?