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mahmit2012
Group Title
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
 2 years ago
 2 years ago
mahmit2012 Group Title
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
 2 years ago
 2 years ago

This Question is Closed

mahmit2012 Group TitleBest ResponseYou've already chosen the best response.0
dw:1337454011771:dw
 2 years ago

mahmit2012 Group TitleBest ResponseYou've already chosen the best response.0
It is not easy to find out.!
 2 years ago

experimentX Group TitleBest 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
 2 years ago

mahmit2012 Group TitleBest ResponseYou've already chosen the best response.0
experimentX can you give me a way to your answer?
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
the left hand derivative must be equal to right hand derivative at x=1
 2 years ago

experimentX Group TitleBest 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
 2 years ago

niravshah08 Group TitleBest 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
 2 years ago

mahmit2012 Group TitleBest ResponseYou've already chosen the best response.0
I know but how can you reach to 1/6 ?
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
wolfram is pretty handy ... :D
 2 years ago

mahmit2012 Group TitleBest ResponseYou've already chosen the best response.0
yeap,but I didn't find any ways in there.
 2 years ago

niravshah08 Group TitleBest ResponseYou've already chosen the best response.0
dw:1337455871084:dw
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
\[ a = \left ( \frac{d}{dx} \left ( \frac{\cos^{1}(\sqrt{x})}{\sqrt{1x}} \right ) \right )_{x=1} \]
 2 years ago

mahmit2012 Group TitleBest ResponseYou've already chosen the best response.0
Ok find it out?it gets so complexity.Doesn't it?
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
\[ \lim_{x>1}ax+b = \lim_{x>1}\frac{\cos^{1}(\sqrt{x})}{\sqrt{1x}}\]
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
i prefer to find out by using wolfram first .. then use hand to verity it.
 2 years ago

experimentX Group TitleBest 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
 2 years ago

mahmit2012 Group TitleBest 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
 2 years ago

asnaseer Group TitleBest 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+
 2 years ago

experimentX Group TitleBest 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
 2 years ago

mahmit2012 Group TitleBest ResponseYou've already chosen the best response.0
please show me 1/6 . I didn't find it in wolfram...!Did you see any?
 2 years ago

asnaseer Group TitleBest 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.
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
sorry  I meant take the limit as x tends to 1
 2 years ago

mahmit2012 Group TitleBest ResponseYou've already chosen the best response.0
Ok copy past the answer and find it out for x=1.
 2 years ago

asnaseer Group TitleBest 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
 2 years ago

mahmit2012 Group TitleBest ResponseYou've already chosen the best response.0
That was wrong site you posted.
 2 years ago

experimentX Group TitleBest 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
 2 years ago

asnaseer Group TitleBest 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 :)
 2 years ago

mahmit2012 Group TitleBest 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)
 2 years ago

mahmit2012 Group TitleBest ResponseYou've already chosen the best response.0
only i looked the answer 1/6 and derivation of function.
 2 years ago

experimentX Group TitleBest 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
 2 years ago

mahmit2012 Group TitleBest ResponseYou've already chosen the best response.0
there is no calculation i chose step but there is only answer.
 2 years ago

mahmit2012 Group TitleBest ResponseYou've already chosen the best response.0
I accepted the conclusion but show me how?
 2 years ago

experimentX Group TitleBest 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??
 2 years ago

experimentX Group TitleBest 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.
 2 years ago

mahmit2012 Group TitleBest ResponseYou've already chosen the best response.0
ok find out this limitdw:1337458049743:dw
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
yeah, that would be 1/6
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
using L'hospital's rule
 2 years ago

mahmit2012 Group TitleBest ResponseYou've already chosen the best response.0
ok show me.i really appreciate
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
are you having trouble with limits?
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
which part .. first or last??
 2 years ago

mahmit2012 Group TitleBest ResponseYou've already chosen the best response.0
no but this is not easy to find out.check it out.
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
Ah sorry ... we need only right hand limit
 2 years ago

mahmit2012 Group TitleBest ResponseYou've already chosen the best response.0
both of them to each other you should take limit,because each goes to infinity !
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
ah .. yes ... looks like i'm nuts
 2 years ago

experimentX Group TitleBest 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
 2 years ago

mahmit2012 Group TitleBest ResponseYou've already chosen the best response.0
im waiting yet.
 2 years ago

experimentX Group TitleBest 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
 2 years ago

mahmit2012 Group TitleBest ResponseYou've already chosen the best response.0
yes it is going to 0/0 so what is the rest?
 2 years ago

mahmit2012 Group TitleBest ResponseYou've already chosen the best response.0
dw:1337460455981:dw
 2 years ago

mahmit2012 Group TitleBest ResponseYou've already chosen the best response.0
dw:1337460652950:dw
 2 years ago

mahmit2012 Group TitleBest ResponseYou've already chosen the best response.0
dw:1337460769484:dw
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
Ahh ... looks like you got it!! good night!!
 2 years ago

mahmit2012 Group TitleBest ResponseYou've already chosen the best response.0
dw:1337460890186:dw
 2 years ago
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