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 2 years 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
 2 years 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

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

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

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

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

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

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

niravshah08
 2 years ago
Best ResponseYou've already chosen the best response.0the right hand derivative is just "a" and left hand derivative can be found using quotient rule

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

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

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

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

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

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

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

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

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

mahmit2012
 2 years ago
Best ResponseYou've already chosen the best response.0in right hand side the limit is going to be 1 .then a+b=1 but give me a proof for a=1/6

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.1you 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+

experimentX
 2 years ago
Best 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

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

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

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

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

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.1you 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

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

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1Jeez 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

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

mahmit2012
 2 years ago
Best ResponseYou've already chosen the best response.0I have never found it yet.so could you please copy past the way (lim x>1)

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

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1it 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

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

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

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1Oh ... 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??

experimentX
 2 years ago
Best 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.

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

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

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

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

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

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

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

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

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

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

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1It 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

experimentX
 2 years ago
Best 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

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

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

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

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

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

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