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Q3
If f(x) is a differentiable at x=1, find a,b.
f(x)=ArcCos(sqrt(x))/sqrt(1x) for 0<=x<1
ax+b for x=>1
 one year ago
 one year ago
Q3 If f(x) is a differentiable at x=1, find a,b. f(x)=ArcCos(sqrt(x))/sqrt(1x) for 0<=x<1 ax+b for x=>1
 one year ago
 one year ago

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mahmit2012Best ResponseYou've already chosen the best response.0
dw:1337454011771:dw
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.0
It is not easy to find out.!
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
a = http://www.wolframalpha.com/input/?i=d%2Fdx+Cos^1%28sqrt%28x%29%29%2Fsqrt%281x%29+%2C+x%3D1
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.0
experimentX can you give me a way to your answer?
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
the left hand derivative must be equal to right hand derivative at x=1
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
for b, the function must be continuous ... so equate left hand limit to right hand limit at x=1
 one year ago

niravshah08Best ResponseYou've already chosen the best response.0
the right hand derivative is just "a" and left hand derivative can be found using quotient rule
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.0
I know but how can you reach to 1/6 ?
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
wolfram is pretty handy ... :D
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.0
yeap,but I didn't find any ways in there.
 one year ago

niravshah08Best ResponseYou've already chosen the best response.0
dw:1337455871084:dw
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
\[ a = \left ( \frac{d}{dx} \left ( \frac{\cos^{1}(\sqrt{x})}{\sqrt{1x}} \right ) \right )_{x=1} \]
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.0
Ok find it out?it gets so complexity.Doesn't it?
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
\[ \lim_{x>1}ax+b = \lim_{x>1}\frac{\cos^{1}(\sqrt{x})}{\sqrt{1x}}\]
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
i prefer to find out by using wolfram first .. then use hand to verity it.
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
http://www.wolframalpha.com/input/?i=lim+x%3E1+Cos^1%28sqrt%28x%29%29%2Fsqrt%281x%29
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.0
in right hand side the limit is going to be 1 .then a+b=1 but give me a proof for a=1/6
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
you can find the proof using wolfram  click show steps to see how it is done: http://www.wolframalpha.com/input/?i=d%2Fdx+Cos^1%28sqrt%28x%29%29%2Fsqrt%281x%29+
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
\[ \left ( \frac{d}{dx}(ax+b) \right )_{x=1} = a = \left ( \frac{d}{dx} \left ( \frac{\cos^{1}(\sqrt{x})}{\sqrt{1x}} \right ) \right )_{x=1}\] http://www.wolframalpha.com/input/?i=d%28Cos^1%28sqrt%28x%29%29%2Fsqrt%281x%29%29%2Fdx+%2C+x%3D1
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.0
please show me 1/6 . I didn't find it in wolfram...!Did you see any?
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
The link I pasted above shows how to find the derivative. Then just plug x=1 into this to get your answer.
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
sorry  I meant take the limit as x tends to 1
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.0
Ok copy past the answer and find it out for x=1.
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
you can find the derivation of this limit here: http://www.wolframalpha.com/input/?i=limit+%281%2F%28%281+%2B+x%29+Sqrt[x]%29+%2B+ArcCos[Sqrt[x]]%2F%281++x%29^%283%2F2%29%29%2F2+as+x+tends+to+1 again, just click show steps to see it
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.0
That was wrong site you posted.
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
Jeez what am i getting instead of indeterminate http://www.wolframalpha.com/input/?i=1%2F2+%281%2F%28%281%2Bx%29+sqrt%28x%29%29%2B%28cos^%281%29%28sqrt%28x%29%29%29%2F%281x%29^%283%2F2%29%29+where+x%3D1
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
experimentX: thats interesting  looks like wolfram is automagically using the limit as x tends to 1 to calculate this :)
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.0
I have never found it yet.so could you please copy past the way (lim x>1)
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.0
only i looked the answer 1/6 and derivation of function.
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
it seems the case http://www.wolframalpha.com/input/?i=lim+x%3E1++1%2F2%281%2F%28%281%2Bx%29+sqrt%28x%29%29%2B%28cos^%281%29%28sqrt%28x%29%29%29%2F%281x%29^%283%2F2%29%29 but limit of derivative ... sounds fisht @mahmit2012 click Show Steps .. below "=" icon
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.0
there is no calculation i chose step but there is only answer.
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.0
I accepted the conclusion but show me how?
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
Oh ... this is a bit fishy ... the slope of f(x) will be a at x=1 (left hand slope as well as slope) While on the other side, the right hand slope tends to this value 'a' ... i think limiting the value of the derivative will just do fine. You can find the derivative of arccos... right??
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
\[ \frac{d}{dx} \left ( \frac{\cos^{1}(\sqrt{x})}{\sqrt{1x}} \right ) \] I mean find this first.
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.0
ok find out this limitdw:1337458049743:dw
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
yeah, that would be 1/6
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
using L'hospital's rule
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.0
ok show me.i really appreciate
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
are you having trouble with limits?
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
which part .. first or last??
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.0
no but this is not easy to find out.check it out.
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
Ah sorry ... we need only right hand limit
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.0
both of them to each other you should take limit,because each goes to infinity !
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
ah .. yes ... looks like i'm nuts
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
It seems to be the case of \( \infty  \infty \) so we can apply L"hospital's rule \[ \frac{1}{(1+x) \sqrt x} = \frac{1}{(1x) \sqrt x}\] make them a fraction ... and use L'hospital's rule
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
\[ \frac{\sqrt x \cos^{1}(\sqrt x)  \sqrt{1x} }{(1x)^{3/2} \sqrt x }\] Use L'hospital rule ... Since now both numerators are denominators are zero ... you can use L'Hospital rule http://www.wolframalpha.com/input/?i=lim+x%3E1++%28sqrt%281x%29+++sqrt%28x%29+cos^1%28sqrt%28x%29%29%29
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.0
yes it is going to 0/0 so what is the rest?
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.0
dw:1337460455981:dw
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.0
dw:1337460652950:dw
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.0
dw:1337460769484:dw
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
Ahh ... looks like you got it!! good night!!
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.0
dw:1337460890186:dw
 one year ago
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