Mister Exam
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- Curve in 3D space defined parametrically
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- The intersection points of functions
-
How to use it?
- Graphing y =:
- x^3+3x^2-9x
- sqrt(2x-1)
-
4x^3-2x^2
- y=x^2-7x+14
- Integral of d{x}:
-
sqrt(2x-1)
- Derivative of:
-
sqrt(2x-1)
-
Identical expressions
- sqrt(2x- one)
- square root of (2x minus 1)
- square root of (2x minus one)
- √(2x-1)
- sqrt2x-1
-
Similar expressions
- sqrt(2*x-1)
- (3*x-15)/(sqrt(2*x)-1-3)
- sqrt(2x+1)
Graphing y = sqrt(2x-1)
The solution
You have entered
[src]
_________ f(x) = \/ 2*x - 1
$$f{\left(x \right)} = \sqrt{2 x - 1}$$
f = sqrt(2*x - 1)
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:
$$\sqrt{2 x - 1} = 0$$
Solve this equation
The points of intersection with the axis X:
Analytical solution
$$x_{1} = \frac{1}{2}$$
Numerical solution
$$x_{1} = 0.5$$
so we need to solve the equation:
$$\sqrt{2 x - 1} = 0$$
Solve this equation
The points of intersection with the axis X:
Analytical solution
$$x_{1} = \frac{1}{2}$$
Numerical solution
$$x_{1} = 0.5$$
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
$$\frac{1}{\sqrt{2 x - 1}} = 0$$
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
$$\frac{1}{\sqrt{2 x - 1}} = 0$$
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
$$- \frac{1}{\left(2 x - 1\right)^{\frac{3}{2}}} = 0$$
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
$$- \frac{1}{\left(2 x - 1\right)^{\frac{3}{2}}} = 0$$
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 x->+oo and x->-oo
$$\lim_{x \to -\infty} \sqrt{2 x - 1} = \infty i$$
Let's take the limit
so,
horizontal asymptote on the left doesn’t exist
$$\lim_{x \to \infty} \sqrt{2 x - 1} = \infty$$
Let's take the limit
so,
horizontal asymptote on the right doesn’t exist
$$\lim_{x \to -\infty} \sqrt{2 x - 1} = \infty i$$
Let's take the limit
so,
horizontal asymptote on the left doesn’t exist
$$\lim_{x \to \infty} \sqrt{2 x - 1} = \infty$$
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(2*x - 1), divided by x at x->+oo and x ->-oo
$$\lim_{x \to -\infty}\left(\frac{\sqrt{2 x - 1}}{x}\right) = 0$$
Let's take the limit
so,
inclined coincides with the horizontal asymptote on the right
$$\lim_{x \to \infty}\left(\frac{\sqrt{2 x - 1}}{x}\right) = 0$$
Let's take the limit
so,
inclined coincides with the horizontal asymptote on the left
$$\lim_{x \to -\infty}\left(\frac{\sqrt{2 x - 1}}{x}\right) = 0$$
Let's take the limit
so,
inclined coincides with the horizontal asymptote on the right
$$\lim_{x \to \infty}\left(\frac{\sqrt{2 x - 1}}{x}\right) = 0$$
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(-x) и f = -f(-x).
So, check:
$$\sqrt{2 x - 1} = \sqrt{- 2 x - 1}$$
- No
$$\sqrt{2 x - 1} = - \sqrt{- 2 x - 1}$$
- No
so, the function
not is
neither even, nor odd
So, check:
$$\sqrt{2 x - 1} = \sqrt{- 2 x - 1}$$
- No
$$\sqrt{2 x - 1} = - \sqrt{- 2 x - 1}$$
- No
so, the function
not is
neither even, nor odd