anonymous
  • anonymous
prove, f(x)=xcos1/x (when x not = 2) =0 (when x=0) f(x) is continuous at the point x=0
Mathematics
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
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anonymous
  • anonymous
is your function f(x)=xcos(1/x) (when x not 0) =0 when x=0 ?
anonymous
  • anonymous
yes yes. i am wrong xnot 0
anonymous
  • anonymous
\[\lim_{x \rightarrow 0+}xcos(1/x)=\lim_{x \rightarrow 0-}xcos(1/x)=f(0)=0\] hence continuous at x=0.

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anonymous
  • anonymous
if you are wondering why \[\lim_{x \rightarrow 0+}xcos(1/x)=0\] then note that \[-1\leq \cos(1/x)\leq 1\ for\ all\ x.\] So \[\lim_{x \rightarrow 0}xcos(1/x)=\lim_{x \rightarrow 0}x\cdot a=a \lim_{x \rightarrow 0}x=0\] here a is any real value between -1 and 1.
anonymous
  • anonymous
thanks
anonymous
  • anonymous
in which class u are?
anonymous
  • anonymous
class 11.u?
anonymous
  • anonymous
me in college 1st year:) which city u?
anonymous
  • anonymous
kolkata
anonymous
  • anonymous
whic school..i am in kolkata
anonymous
  • anonymous
khidirpur st.thomas
anonymous
  • anonymous
cbse? if u need help regarding math problems u can ask me! i can suggest a great math book for classes 11 and 12!
anonymous
  • anonymous
oh , say the name.can u suggest some books for mathematical olympiad?
anonymous
  • anonymous
your college?
anonymous
  • anonymous
yeah! I am in Jadavpur University (Mech Engg) for school to IIT level problems: Problems Plus In IIT Mathematics by Asit Dasgupta
anonymous
  • anonymous
the book by asit dasgupta is great for the basics but for RMO,INMO u need to try some other books...
anonymous
  • anonymous
did u appear for RMO/INMO any time.
anonymous
  • anonymous
yes one time in class 11:was not well prepared:( didnt get through...u need tough preparations for RMO...however if u r a genius u dont need much preparataions!
anonymous
  • anonymous
are u good in probability?it is tough to me.
anonymous
  • anonymous
u can try me. :)
anonymous
  • anonymous
i have no hard problem at present.when i found a very hard problem,i would ask u .
anonymous
  • anonymous
u can call me (if u want my cell no. u can ask me now) or u can mail me to saubhik.mukherjee@gmail.com...i dont come to openstudy often..so u can take my phone no. or gmail
anonymous
  • anonymous
ok.i will mail u.however do u have interest in astrophysics.it is my most fav.
anonymous
  • anonymous
about me: i got 100 in maths in class 12 and 100 in class 10 CBSE. I love olympiad mathematics and want to help anyone interested in olympiad maths. about astrophysics:there is an olympiad for that and I dont know anything about it :)
anonymous
  • anonymous
wow.u r so brilliant!
anonymous
  • anonymous
thanks.hope to help u soon :)
anonymous
  • anonymous
in triangle ABC,AB=AC,A is right angle.M & N are 2points on BC satisfying BM^2+CN^2=MN^2. prove that angle MAN=45.
anonymous
  • anonymous
I proved it using coordinate geometry. Did not get a good pure geometry solution though. I can show you the proof. You can post this as a separate question.
anonymous
  • anonymous
show
anonymous
  • anonymous
wait...i will attach a picture wait 2 min.
anonymous
  • anonymous
see
1 Attachment
anonymous
  • anonymous
did u see the picture? The side AB is on y-axis and AC is on x-axis...
anonymous
  • anonymous
yes i did and understand.thanks a lot !!!but whenever u get pure geometry solution please post,30 MEDALS for u.
anonymous
  • anonymous
i did not explain anything..u got it? u have to use the distance formula to obtain a relation and then use this relation in another equation which u will get by considering the angle between the two lines AM and AN, which u can get by considering the slopes of the two lines AM and AN. did u get this angle as 45 degrees?
anonymous
  • anonymous
what's your e-mail id?
anonymous
  • anonymous
yes my elder sister helped me
anonymous
  • anonymous
anonymous
  • anonymous
ok...any more problems u can always ask me:)
anonymous
  • anonymous
i will.buy

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