A community for students.
Here's the question you clicked on:
 0 viewing
mahmit2012
 3 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
mahmit2012
 3 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

This Question is Closed

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

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

experimentX
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.0experimentX can you give me a way to your answer?

experimentX
 3 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
 3 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
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.0I know but how can you reach to 1/6 ?

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

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

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

experimentX
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.0Ok find it out?it gets so complexity.Doesn't it?

experimentX
 3 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
 3 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
 3 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
 3 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
 3 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
 3 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
 3 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
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.1sorry  I meant take the limit as x tends to 1

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

asnaseer
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.0That was wrong site you posted.

experimentX
 3 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
 3 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
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.0only i looked the answer 1/6 and derivation of function.

experimentX
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.0there is no calculation i chose step but there is only answer.

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

experimentX
 3 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
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.0ok find out this limitdw:1337458049743:dw

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

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

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

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

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

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

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

mahmit2012
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.1ah .. yes ... looks like i'm nuts

experimentX
 3 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
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.0yes it is going to 0/0 so what is the rest?

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

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

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

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

mahmit2012
 3 years ago
Best ResponseYou've already chosen the best response.0dw:1337460890186:dw
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.