ahmet Posted August 20, 2020 Share Posted August 20, 2020 (edited) 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 Link to comment Share on other sites More sharing options...

mathematic Posted August 21, 2020 Share Posted August 21, 2020 log has discontinuity at 0. arc ? - what do you mean? Link to comment Share on other sites More sharing options...

ahmet Posted August 21, 2020 Author Share Posted August 21, 2020 (edited) 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 Link to comment Share on other sites More sharing options...

HallsofIvy Posted October 13, 2020 Share Posted October 13, 2020 "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 More sharing options...

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