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prove, f(x)=xcos1/x (when x not = 2) =0 (when x=0) f(x) is continuous at the point x=0

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is your function f(x)=xcos(1/x) (when x not 0) =0 when x=0 ?
yes yes. i am wrong xnot 0
\[\lim_{x \rightarrow 0+}xcos(1/x)=\lim_{x \rightarrow 0-}xcos(1/x)=f(0)=0\] hence continuous at x=0.

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Other answers:

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.
in which class u are?
class 11.u?
me in college 1st year:) which city u?
whic school..i am in kolkata
khidirpur st.thomas
cbse? if u need help regarding math problems u can ask me! i can suggest a great math book for classes 11 and 12!
oh , say the name.can u suggest some books for mathematical olympiad?
your college?
yeah! I am in Jadavpur University (Mech Engg) for school to IIT level problems: Problems Plus In IIT Mathematics by Asit Dasgupta
the book by asit dasgupta is great for the basics but for RMO,INMO u need to try some other books...
did u appear for RMO/INMO any time.
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!
are u good in probability?it is tough to me.
u can try me. :)
i have no hard problem at present.when i found a very hard problem,i would ask u .
u can call me (if u want my cell no. u can ask me now) or u can mail me to dont come to openstudy u can take my phone no. or gmail
ok.i will mail u.however do u have interest in is my most fav.
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 :)
wow.u r so brilliant!
thanks.hope to help u soon :)
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.
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.
wait...i will attach a picture wait 2 min.
1 Attachment
did u see the picture? The side AB is on y-axis and AC is on x-axis...
yes i did and understand.thanks a lot !!!but whenever u get pure geometry solution please post,30 MEDALS for u.
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?
what's your e-mail id?
yes my elder sister helped me
ok...any more problems u can always ask me:)

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