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 =:
-
y=|x-2|-|x+1|+x-2
-
4x/(x^2+1)^2
- -1/3x^3+4x
- x^4-2*x^2-3
- Integral of d{x}:
-
sqrt(y)
- Derivative of:
-
sqrt(y)
- Limit of the function:
- sqrt(y)
-
Identical expressions
- sqrt(y)
- square root of (y)
- √(y)
- sqrty
-
Similar expressions
- sqrt(y^2+1)/y
- sqrt(y+4)
- 9-2sqrt(y^2+4y+8)
- -sqrt(y+1)
- sqrt(y^2+4*y-12)
Graphing y = sqrt(y)
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:
$$\sqrt{y} = 0$$
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:
$$\sqrt{y} = 0$$
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
$$\frac{1}{2 \sqrt{y}} = 0$$
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
$$\frac{1}{2 \sqrt{y}} = 0$$
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
$$- \frac{1}{4 y^{\frac{3}{2}}} = 0$$
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
$$- \frac{1}{4 y^{\frac{3}{2}}} = 0$$
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
$$\lim_{y \to -\infty} \sqrt{y} = \infty i$$
Let's take the limit
so,
horizontal asymptote on the left doesn’t exist
$$\lim_{y \to \infty} \sqrt{y} = \infty$$
Let's take the limit
so,
horizontal asymptote on the right doesn’t exist
$$\lim_{y \to -\infty} \sqrt{y} = \infty i$$
Let's take the limit
so,
horizontal asymptote on the left doesn’t exist
$$\lim_{y \to \infty} \sqrt{y} = \infty$$
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 sqrt(y), divided by y at y->+oo and y ->-oo
$$\lim_{y \to -\infty} \frac{1}{\sqrt{y}} = 0$$
Let's take the limit
so,
inclined coincides with the horizontal asymptote on the right
$$\lim_{y \to \infty} \frac{1}{\sqrt{y}} = 0$$
Let's take the limit
so,
inclined coincides with the horizontal asymptote on the left
$$\lim_{y \to -\infty} \frac{1}{\sqrt{y}} = 0$$
Let's take the limit
so,
inclined coincides with the horizontal asymptote on the right
$$\lim_{y \to \infty} \frac{1}{\sqrt{y}} = 0$$
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(-y) и f = -f(-y).
So, check:
$$\sqrt{y} = \sqrt{- y}$$
- No
$$\sqrt{y} = - \sqrt{- y}$$
- No
so, the function
not is
neither even, nor odd
So, check:
$$\sqrt{y} = \sqrt{- y}$$
- No
$$\sqrt{y} = - \sqrt{- y}$$
- No
so, the function
not is
neither even, nor odd