Mister Exam
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-
How to use it?
- Graphing y =:
- ((x^2+x-6)(x^2-2x-3))/(x^2-9)
- x^3-12x+24
- (x^2+5)/(x-2)
-
|x+7|
-
Identical expressions
- arctan((x+ one)/(x+ one))
- arc tangent of ((x plus 1) divide by (x plus 1))
- arc tangent of ((x plus one) divide by (x plus one))
- arctanx+1/x+1
- arctan((x+1) divide by (x+1))
-
Similar expressions
- arctan((x-1)/(x+1))
- arctan((x+1)/(x-1))
Graphing y = arctan((x+1)/(x+1))
The solution
You have entered
[src]
/x + 1\
f(x) = atan|-----|
\x + 1/
$$f{\left(x \right)} = \operatorname{atan}{\left(\frac{x + 1}{x + 1} \right)}$$
f = atan((x + 1)/(x + 1))
The domain of the function
The points at which the function is not precisely defined:
$$x_{1} = -1$$
$$x_{1} = -1$$
The points of intersection with the X-axis coordinate
Graph of the function intersects the axis X at f = 0
so we need to solve the equation:
$$\operatorname{atan}{\left(\frac{x + 1}{x + 1} \right)} = 0$$
Solve this equation
Solution is not found,
it's possible that the graph doesn't intersect the axis X
so we need to solve the equation:
$$\operatorname{atan}{\left(\frac{x + 1}{x + 1} \right)} = 0$$
Solve this equation
Solution is not found,
it's possible that the graph doesn't intersect the axis X
Extrema of the function
In order to find the extrema, we need to solve the equation
$$\frac{d}{d x} f{\left(x \right)} = 0$$
(the derivative equals zero),
and the roots of this equation are the extrema of this function:
$$\frac{d}{d x} f{\left(x \right)} = $$
the first derivative
$$0 = 0$$
Solve this equation
Solutions are not found,
function may have no extrema
$$\frac{d}{d x} f{\left(x \right)} = 0$$
(the derivative equals zero),
and the roots of this equation are the extrema of this function:
$$\frac{d}{d x} f{\left(x \right)} = $$
the first derivative
$$0 = 0$$
Solve this equation
Solutions are not found,
function may have no extrema
Inflection points
Let's find the inflection points, we'll need to solve the equation for this
$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = 0$$
(the second derivative equals zero),
the roots of this equation will be the inflection points for the specified function graph:
$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = $$
the second derivative
$$0 = 0$$
Solve this equation
Solutions are not found,
maybe, the function has no inflections
$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = 0$$
(the second derivative equals zero),
the roots of this equation will be the inflection points for the specified function graph:
$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = $$
the second derivative
$$0 = 0$$
Solve this equation
Solutions are not found,
maybe, the function has no inflections
Vertical asymptotes
Have:
$$x_{1} = -1$$
$$x_{1} = -1$$
Horizontal asymptotes
Let’s find horizontal asymptotes with help of the limits of this function at x->+oo and x->-oo
$$\lim_{x \to -\infty} \operatorname{atan}{\left(\frac{x + 1}{x + 1} \right)} = \frac{\pi}{4}$$
Let's take the limit
so,
equation of the horizontal asymptote on the left:
$$y = \frac{\pi}{4}$$
$$\lim_{x \to \infty} \operatorname{atan}{\left(\frac{x + 1}{x + 1} \right)} = \frac{\pi}{4}$$
Let's take the limit
so,
equation of the horizontal asymptote on the right:
$$y = \frac{\pi}{4}$$
$$\lim_{x \to -\infty} \operatorname{atan}{\left(\frac{x + 1}{x + 1} \right)} = \frac{\pi}{4}$$
Let's take the limit
so,
equation of the horizontal asymptote on the left:
$$y = \frac{\pi}{4}$$
$$\lim_{x \to \infty} \operatorname{atan}{\left(\frac{x + 1}{x + 1} \right)} = \frac{\pi}{4}$$
Let's take the limit
so,
equation of the horizontal asymptote on the right:
$$y = \frac{\pi}{4}$$
Inclined asymptotes
Inclined asymptote can be found by calculating the limit of atan((x + 1)/(x + 1)), divided by x at x->+oo and x ->-oo
$$\lim_{x \to -\infty}\left(\frac{\operatorname{atan}{\left(\frac{x + 1}{x + 1} \right)}}{x}\right) = 0$$
Let's take the limit
so,
inclined coincides with the horizontal asymptote on the right
$$\lim_{x \to \infty}\left(\frac{\operatorname{atan}{\left(\frac{x + 1}{x + 1} \right)}}{x}\right) = 0$$
Let's take the limit
so,
inclined coincides with the horizontal asymptote on the left
$$\lim_{x \to -\infty}\left(\frac{\operatorname{atan}{\left(\frac{x + 1}{x + 1} \right)}}{x}\right) = 0$$
Let's take the limit
so,
inclined coincides with the horizontal asymptote on the right
$$\lim_{x \to \infty}\left(\frac{\operatorname{atan}{\left(\frac{x + 1}{x + 1} \right)}}{x}\right) = 0$$
Let's take the limit
so,
inclined coincides with the horizontal asymptote on the left
Even and odd functions
Let's check, whether the function even or odd by using relations f = f(-x) и f = -f(-x).
So, check:
$$\operatorname{atan}{\left(\frac{x + 1}{x + 1} \right)} = \frac{\pi}{4}$$
- No
$$\operatorname{atan}{\left(\frac{x + 1}{x + 1} \right)} = - \frac{\pi}{4}$$
- No
so, the function
not is
neither even, nor odd
So, check:
$$\operatorname{atan}{\left(\frac{x + 1}{x + 1} \right)} = \frac{\pi}{4}$$
- No
$$\operatorname{atan}{\left(\frac{x + 1}{x + 1} \right)} = - \frac{\pi}{4}$$
- No
so, the function
not is
neither even, nor odd