Mister Exam
Other calculators
- Graph of implicit function
- Derivative Step by Step
- Integral Step by Step
- Graph of parametric function
- Graph in Polar Coordinates
- Surface defined parametrically
- Surface defined by equation
- Curve in 3D space defined parametrically
- Area between lines
- The intersection points of functions
-
How to use it?
- Graphing y =:
- (x+2)/((x^2+16)×(x^2-1))
- x^3-12x+24
- -x^2+5x+4
- -x^2+5*x+4
- Integral of d{x}:
-
2*t
-
Identical expressions
- two *t
- 2 multiply by t
- two multiply by t
- 2t
-
Similar expressions
- -2tg(x-1)+3
- 2tg(x/4)/(1+(tg(x/4))^2)
Graphing y = 2*t
The solution
The graph of the function
The points of intersection with the X-axis coordinate
Graph of the function intersects the axis T at f = 0
so we need to solve the equation:
$$2 t = 0$$
Solve this equation
The points of intersection with the axis T:
Analytical solution
$$t_{1} = 0$$
Numerical solution
$$t_{1} = 0$$
so we need to solve the equation:
$$2 t = 0$$
Solve this equation
The points of intersection with the axis T:
Analytical solution
$$t_{1} = 0$$
Numerical solution
$$t_{1} = 0$$
Extrema of the function
In order to find the extrema, we need to solve the equation
$$\frac{d}{d t} f{\left(t \right)} = 0$$
(the derivative equals zero),
and the roots of this equation are the extrema of this function:
$$\frac{d}{d t} f{\left(t \right)} = $$
the first derivative
$$2 = 0$$
Solve this equation
Solutions are not found,
function may have no extrema
$$\frac{d}{d t} f{\left(t \right)} = 0$$
(the derivative equals zero),
and the roots of this equation are the extrema of this function:
$$\frac{d}{d t} f{\left(t \right)} = $$
the first derivative
$$2 = 0$$
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
$$\frac{d^{2}}{d t^{2}} f{\left(t \right)} = 0$$
(the second derivative equals zero),
the roots of this equation will be the inflection points for the specified function graph:
$$\frac{d^{2}}{d t^{2}} f{\left(t \right)} = $$
the second derivative
$$0 = 0$$
Solve this equation
Solutions are not found,
maybe, the function has no inflections
$$\frac{d^{2}}{d t^{2}} f{\left(t \right)} = 0$$
(the second derivative equals zero),
the roots of this equation will be the inflection points for the specified function graph:
$$\frac{d^{2}}{d t^{2}} f{\left(t \right)} = $$
the second derivative
$$0 = 0$$
Solve this equation
Solutions are not found,
maybe, the function has no inflections
Horizontal asymptotes
Let’s find horizontal asymptotes with help of the limits of this function at t->+oo and t->-oo
$$\lim_{t \to -\infty}\left(2 t\right) = -\infty$$
Let's take the limit
so,
horizontal asymptote on the left doesn’t exist
$$\lim_{t \to \infty}\left(2 t\right) = \infty$$
Let's take the limit
so,
horizontal asymptote on the right doesn’t exist
$$\lim_{t \to -\infty}\left(2 t\right) = -\infty$$
Let's take the limit
so,
horizontal asymptote on the left doesn’t exist
$$\lim_{t \to \infty}\left(2 t\right) = \infty$$
Let's take the limit
so,
horizontal asymptote on the right doesn’t exist
Inclined asymptotes
Inclined asymptote can be found by calculating the limit of 2*t, divided by t at t->+oo and t ->-oo
$$\lim_{t \to -\infty} 2 = 2$$
Let's take the limit
so,
inclined asymptote equation on the left:
$$y = 2 t$$
$$\lim_{t \to \infty} 2 = 2$$
Let's take the limit
so,
inclined asymptote equation on the right:
$$y = 2 t$$
$$\lim_{t \to -\infty} 2 = 2$$
Let's take the limit
so,
inclined asymptote equation on the left:
$$y = 2 t$$
$$\lim_{t \to \infty} 2 = 2$$
Let's take the limit
so,
inclined asymptote equation on the right:
$$y = 2 t$$
Even and odd functions
Let's check, whether the function even or odd by using relations f = f(-t) и f = -f(-t).
So, check:
$$2 t = - 2 t$$
- No
$$2 t = 2 t$$
- Yes
so, the function
is
odd
So, check:
$$2 t = - 2 t$$
- No
$$2 t = 2 t$$
- Yes
so, the function
is
odd