Jump to content

elementary functions and limits


ahmet
 Share

Recommended Posts

hi,

I do not remember whether any function given in this category has had discontinuoum point. But with one notation: [math] -\infty, \infty  [/math] are accepted as points. (This is real analysis)

thus if any point accepts its limit  one of these points,then this is not a problem. (however, one point cannot accept both of these points as limit point ,because this will be accepted as discontinuoum)

 

elementary functions : LAPTE

L: logaritmic

A: arc 

P: polynomic

T: trygnometric

E: exponential. 

thanks.

 

 

Edited by ahmet
Link to comment
Share on other sites

12 hours ago, mathematic said:

log has discontinuity at 0.  arc ? - what do you mean?

as it explained we will accept [math] -\infty,\infty [/math] as points. Thus this is not a type of discontinuity. (but if any case be occured like right limit and left limit are different points then this will be discontinuity.)

 

and arc means inverse trygonometric functions (e.g. arcsin(x) ,arccos(2x), etc)

Edited by ahmet
Link to comment
Share on other sites

  • 1 month later...

 

"L: logaritmic" log(x) is continuous for x any positive number, not defined for x non-positive.

"A: arc"  "arc" is not a function, it is a geometric object. 

"P: polynomic" Polnomials are continuous for all x.

"T: trygnometric " sine and cosine are conntinuous for all x.  tangent is continuous for all x except multiples of pi,  cotangent is continuous for all odd multiples of pi/2.  secant is cotinuous for all x except odd multiples of pi/2, and cosecant is continuous for all x except multiples of pi. 

"E: exponential." e^x and the general a^x, for positive a, is continuous for all x.

Link to comment
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now
 Share

×
×
  • Create New...

Important Information

We have placed cookies on your device to help make this website better. You can adjust your cookie settings, otherwise we'll assume you're okay to continue.