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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- Nov 17th 2010, 07:39 AMalexandrabel90continuous
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.. - Nov 17th 2010, 08:53 AMchisigma
The function has a singularity for so that Your function has a singularity for x satisfying the equation . One solution is

Kind regards

- Nov 17th 2010, 08:59 AMalexandrabel90
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..

- Nov 17th 2010, 09:00 AMFernandoRevilla
The function:

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. - Nov 17th 2010, 09:09 AMFernandoRevilla
- Nov 17th 2010, 09:19 AMalexandrabel90
may i know how do i prove this theorem? i never learnt this theorem before. thanks!!

- Nov 17th 2010, 09:47 AMFernandoRevilla
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., ...

Regards.