Mister Exam
Other calculators
- Graph of implicit function
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- Integral Step by Step
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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-1)/(x+5)
- x³+3x²-9x+1
- x^3+3x^2-24x-21
- x³-2x
- Integral of d{x}:
-
y/2
- Derivative of:
-
y/2
- y/2
-
Identical expressions
- y/ two
- y divide by 2
- y divide by two
-
Similar expressions
- 5*sqrt(y)/2
- (6-3y)/2
Graphing y = y/2
The solution
The graph of the function
The points of intersection with the X-axis coordinate
Graph of the function intersects the axis Y at f = 0
so we need to solve the equation:
$$\frac{y}{2} = 0$$
Solve this equation
The points of intersection with the axis Y:
Analytical solution
$$y_{1} = 0$$
Numerical solution
$$y_{1} = 0$$
so we need to solve the equation:
$$\frac{y}{2} = 0$$
Solve this equation
The points of intersection with the axis Y:
Analytical solution
$$y_{1} = 0$$
Numerical solution
$$y_{1} = 0$$
Extrema of the function
In order to find the extrema, we need to solve the equation
$$\frac{d}{d y} f{\left(y \right)} = 0$$
(the derivative equals zero),
and the roots of this equation are the extrema of this function:
$$\frac{d}{d y} f{\left(y \right)} = $$
the first derivative
$$\frac{1}{2} = 0$$
Solve this equation
Solutions are not found,
function may have no extrema
$$\frac{d}{d y} f{\left(y \right)} = 0$$
(the derivative equals zero),
and the roots of this equation are the extrema of this function:
$$\frac{d}{d y} f{\left(y \right)} = $$
the first derivative
$$\frac{1}{2} = 0$$
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
$$\frac{d^{2}}{d y^{2}} f{\left(y \right)} = 0$$
(the second derivative equals zero),
the roots of this equation will be the inflection points for the specified function graph:
$$\frac{d^{2}}{d y^{2}} f{\left(y \right)} = $$
the second derivative
$$0 = 0$$
Solve this equation
Solutions are not found,
maybe, the function has no inflections
$$\frac{d^{2}}{d y^{2}} f{\left(y \right)} = 0$$
(the second derivative equals zero),
the roots of this equation will be the inflection points for the specified function graph:
$$\frac{d^{2}}{d y^{2}} f{\left(y \right)} = $$
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 y->+oo and y->-oo
$$\lim_{y \to -\infty}\left(\frac{y}{2}\right) = -\infty$$
Let's take the limit
so,
horizontal asymptote on the left doesn’t exist
$$\lim_{y \to \infty}\left(\frac{y}{2}\right) = \infty$$
Let's take the limit
so,
horizontal asymptote on the right doesn’t exist
$$\lim_{y \to -\infty}\left(\frac{y}{2}\right) = -\infty$$
Let's take the limit
so,
horizontal asymptote on the left doesn’t exist
$$\lim_{y \to \infty}\left(\frac{y}{2}\right) = \infty$$
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 y/2, divided by y at y->+oo and y ->-oo
$$\lim_{y \to -\infty} \frac{1}{2} = \frac{1}{2}$$
Let's take the limit
so,
inclined asymptote equation on the left:
$$y = \frac{y}{2}$$
$$\lim_{y \to \infty} \frac{1}{2} = \frac{1}{2}$$
Let's take the limit
so,
inclined asymptote equation on the right:
$$y = \frac{y}{2}$$
$$\lim_{y \to -\infty} \frac{1}{2} = \frac{1}{2}$$
Let's take the limit
so,
inclined asymptote equation on the left:
$$y = \frac{y}{2}$$
$$\lim_{y \to \infty} \frac{1}{2} = \frac{1}{2}$$
Let's take the limit
so,
inclined asymptote equation on the right:
$$y = \frac{y}{2}$$
Even and odd functions
Let's check, whether the function even or odd by using relations f = f(-y) и f = -f(-y).
So, check:
$$\frac{y}{2} = - \frac{y}{2}$$
- No
$$\frac{y}{2} = \frac{y}{2}$$
- No
so, the function
not is
neither even, nor odd
So, check:
$$\frac{y}{2} = - \frac{y}{2}$$
- No
$$\frac{y}{2} = \frac{y}{2}$$
- No
so, the function
not is
neither even, nor odd