how do you prove that the unction f(x) = tan(x+x^2)/(1+x+x^2) is continuous for all x=[0,1] except at one point.
i found out that it is not cont at x= 0.84936..but i dont know how to prove that it is continuous now..
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The function has a singularity for so that Your function has a singularity for x satisfying the equation . One solution is
haha ya i knew that it is not continuous at x= 0.84936.. as stated in my question..so, im trying to ask how do i show that it is continuous for all points other than x= 0.84936..
is an elementary function, for all real and does not exists. Solving you'll obtain the point in where is not continuous:
Regards. Edited: Sorry, I didn't see the previous answers.
Last edited by FernandoRevilla; Nov 17th 2010 at 10:34 AM.
Originally Posted by alexandrabel90 ... so, im trying to ask how do i show that it is continuous for all points other than x= 0.84936.. Theorem: If f is an elementary real funtion of real variable, then f is continuos just at the points f is defined.
may i know how do i prove this theorem? i never learnt this theorem before. thanks!!
For example: (i) is continuous in (polynomical function). (ii) is continuous in (polynomical function). (iii) is continuous in (iv) Composition of continuous are continuous.
etc. etc., ...
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