Limits of functions

1)

• maximal domain of definition: $\mathbb{R}$;

• aperiodic function;

• the graph does not meet the Ox axis*;*

• intersection with the Oy axis: (0,1);

• the function is even;

• the Oy axis is a horizontal asymptote;

• is continuous on $\mathbb{R}$;

• also known as the "Gaussian bell curve".

2)

• maximal domain of definition: $\mathbb{R}$;

• periodic function, with fundamental period 2π ;

• the graph meets the Oy axis at (0,1), and the Ox axis at $(k\pi,0); k\in \mathbb{Z}\backslash \{0\}$ ;

• the function is even;

• has no asymptotes;

• it is continuous on $\mathbb{R}$;

• known as the "damped sine".

3)

• maximal domain of definition: $\mathbb{R}\backslash \{0\}$;

• periodic function, with no fundamental period;

• the graph does not meet the Oy axis*;*

• the graph meets the Ox axis at the points

• the function is odd;

• the Oy axis is a vertical asymptote;

• is continuous on $\mathbb{R}\backslash \{0\}$;

• known as the "damped cosine".

4)

• maximal domain of definition: ;

• periodic function, with no fundamental period;

• the graph meets the Oy axis at (0,1);

• the graph meets the Ox axis at the points $(k\pi,0), k\in \mathbb{Z}\backslash \{0\}$;

• the function is even;

• the lines are vertical asymptotes ;

• is continuous on ;

• known as the "damped tangent".

5)

• maximal domain of definition: ;

• periodic function, with no fundamental period;

• the graph does not meet the Oy axis;

• the graph meets the Ox axis at the points ;

• the function is even;

• the lines $x=k\pi, k\in \mathbb{Z}\backslash \{0\}$ are vertical asymptotes ;

• it is continuous on (0, π);

• known as the "damped cotangent".

6)

• maximal domain of definition: $\mathbb{R}$;

• aperiodic function;

• the graph does not meet the Ox axis*;*

• intersection with the Oy axis: (0,1);

• the function is even;

• the Oy axis is a horizontal asymptote;

• is continuous on $\mathbb{R}$;

7)

• maximal domain of definition: $\mathbb{R}$;

• aperiodic function;

• the graph does not meet the Ox axis*;*

• intersection with the Oy axis: (0,1);

• the function is even;

• the Oy axis is a horizontal asymptote;

• is continuous on $\mathbb{R}$;

6)

• maximal domain of definition: $(-1,\infty)$;

• aperiodic function;

• the graph does not meet the Ox axis*;*

• intersection with the Oy axis: (0,1);

• the Oy axis is a horizontal asymptote;

• is continuous on $\mathbb{R}$;

7)

• maximal domain of definition: $\mathbb{R}$;

• aperiodic function;

• the graph does not meet the Ox axis*;*

• intersection with the Oy axis: $(0,ln2)$;

• the Oy axis is a horizontal asymptote;

• is continuous on $\mathbb{R}$;