Mister Exam
Other calculators
- Graph of implicit function
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- Graph in Polar Coordinates
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- 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^4+2x^2+3
- x^4+2x^2+1
- x^4-4x+4
- -x^4+4x^3+1
- Integral of d{x}:
-
-1/t
-
Identical expressions
- - one /t
- minus 1 divide by t
- minus one divide by t
- -1 divide by t
-
Similar expressions
- 1/t
- (-1)/tan(1+x)
- (t-1)/(t+1)
Graphing y = -1/t
The solution
The graph of the function
The domain of the function
The points at which the function is not precisely defined:
$$t_{1} = 0$$
$$t_{1} = 0$$
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:
$$- \frac{1}{t} = 0$$
Solve this equation
Solution is not found,
it's possible that the graph doesn't intersect the axis T
so we need to solve the equation:
$$- \frac{1}{t} = 0$$
Solve this equation
Solution is not found,
it's possible that the graph doesn't intersect the axis T
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
$$\frac{1}{t^{2}} = 0$$
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
$$\frac{1}{t^{2}} = 0$$
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
$$- \frac{2}{t^{3}} = 0$$
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
$$- \frac{2}{t^{3}} = 0$$
Solve this equation
Solutions are not found,
maybe, the function has no inflections
Vertical asymptotes
Have:
$$t_{1} = 0$$
$$t_{1} = 0$$
Horizontal asymptotes
Let’s find horizontal asymptotes with help of the limits of this function at t->+oo and t->-oo
$$\lim_{t \to -\infty}\left(- \frac{1}{t}\right) = 0$$
Let's take the limit
so,
equation of the horizontal asymptote on the left:
$$y = 0$$
$$\lim_{t \to \infty}\left(- \frac{1}{t}\right) = 0$$
Let's take the limit
so,
equation of the horizontal asymptote on the right:
$$y = 0$$
$$\lim_{t \to -\infty}\left(- \frac{1}{t}\right) = 0$$
Let's take the limit
so,
equation of the horizontal asymptote on the left:
$$y = 0$$
$$\lim_{t \to \infty}\left(- \frac{1}{t}\right) = 0$$
Let's take the limit
so,
equation of the horizontal asymptote on the right:
$$y = 0$$
Inclined asymptotes
Inclined asymptote can be found by calculating the limit of -1/t, divided by t at t->+oo and t ->-oo
$$\lim_{t \to -\infty}\left(- \frac{1}{t^{2}}\right) = 0$$
Let's take the limit
so,
inclined coincides with the horizontal asymptote on the right
$$\lim_{t \to \infty}\left(- \frac{1}{t^{2}}\right) = 0$$
Let's take the limit
so,
inclined coincides with the horizontal asymptote on the left
$$\lim_{t \to -\infty}\left(- \frac{1}{t^{2}}\right) = 0$$
Let's take the limit
so,
inclined coincides with the horizontal asymptote on the right
$$\lim_{t \to \infty}\left(- \frac{1}{t^{2}}\right) = 0$$
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(-t) и f = -f(-t).
So, check:
$$- \frac{1}{t} = \frac{1}{t}$$
- No
$$- \frac{1}{t} = - \frac{1}{t}$$
- Yes
so, the function
is
odd
So, check:
$$- \frac{1}{t} = \frac{1}{t}$$
- No
$$- \frac{1}{t} = - \frac{1}{t}$$
- Yes
so, the function
is
odd