elementary functions and limits

[ahmet]

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 August 20, 2020 by ahmet

[mathematic]

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

[ahmet]

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 August 21, 2020 by ahmet

[HallsofIvy]

 

"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.