Mister Exam
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-
How to use it?
- Graphing y =:
- x^3+6*x^2+9*x
- x^3-5/2x^2-2x+3/2
- x^3-3x-2
- x^3+3x-2
- Derivative of:
-
x/10
- Limit of the function:
-
x/10
-
Identical expressions
- x/ ten
- x divide by 10
- x divide by ten
-
Similar expressions
- 2*sin(x)+x+sin(x)/100
- arctan((20x)/(100-x^2))
- 4*(cos(x)+3*x)/10
- (2sin(x)-cos(x))/10(sin(x)+2cos²(x))+(1/10sqrt(5))*ln(tan(x/2)+atan2/2)
Graphing y = x/10
The solution
The graph of the function
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:
$$\frac{x}{10} = 0$$
Solve this equation
The points of intersection with the axis X:
Analytical solution
$$x_{1} = 0$$
Numerical solution
$$x_{1} = 0$$
so we need to solve the equation:
$$\frac{x}{10} = 0$$
Solve this equation
The points of intersection with the axis X:
Analytical solution
$$x_{1} = 0$$
Numerical solution
$$x_{1} = 0$$
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
$$\frac{1}{10} = 0$$
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
$$\frac{1}{10} = 0$$
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
Horizontal asymptotes
Let’s find horizontal asymptotes with help of the limits of this function at x->+oo and x->-oo
$$\lim_{x \to -\infty}\left(\frac{x}{10}\right) = -\infty$$
Let's take the limit
so,
horizontal asymptote on the left doesn’t exist
$$\lim_{x \to \infty}\left(\frac{x}{10}\right) = \infty$$
Let's take the limit
so,
horizontal asymptote on the right doesn’t exist
$$\lim_{x \to -\infty}\left(\frac{x}{10}\right) = -\infty$$
Let's take the limit
so,
horizontal asymptote on the left doesn’t exist
$$\lim_{x \to \infty}\left(\frac{x}{10}\right) = \infty$$
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 x/10, divided by x at x->+oo and x ->-oo
$$\lim_{x \to -\infty} \frac{1}{10} = \frac{1}{10}$$
Let's take the limit
so,
inclined asymptote equation on the left:
$$y = \frac{x}{10}$$
$$\lim_{x \to \infty} \frac{1}{10} = \frac{1}{10}$$
Let's take the limit
so,
inclined asymptote equation on the right:
$$y = \frac{x}{10}$$
$$\lim_{x \to -\infty} \frac{1}{10} = \frac{1}{10}$$
Let's take the limit
so,
inclined asymptote equation on the left:
$$y = \frac{x}{10}$$
$$\lim_{x \to \infty} \frac{1}{10} = \frac{1}{10}$$
Let's take the limit
so,
inclined asymptote equation on the right:
$$y = \frac{x}{10}$$
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:
$$\frac{x}{10} = - \frac{x}{10}$$
- No
$$\frac{x}{10} = \frac{x}{10}$$
- No
so, the function
not is
neither even, nor odd
So, check:
$$\frac{x}{10} = - \frac{x}{10}$$
- No
$$\frac{x}{10} = \frac{x}{10}$$
- No
so, the function
not is
neither even, nor odd