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  • How to use it?

  • Graphing y =:
  • y=log1/5x
  • sqrt(((12*sin(3.14*x*20/1000000)-6*sin(3.14*x*40/1000000))/(4*3.14*x))^2+((18-18*sin(3.14*x*40/1000000))/(4*3.14*x))^2)
  • factorial(x)
  • xe^-((x^2)/2)

  • Identical expressions

  • sqrt(((twelve *sin(three . fourteen *x* twenty / one million)- six *sin(three . fourteen *x* forty / one million))/(four * three . fourteen *x))^ two +((eighteen - eighteen *sin(three . fourteen *x* forty / one million))/(four * three . fourteen *x))^ two)
  • square root of (((12 multiply by sinus of (3.14 multiply by x multiply by 20 divide by 1000000) minus 6 multiply by sinus of (3.14 multiply by x multiply by 40 divide by 1000000)) divide by (4 multiply by 3.14 multiply by x)) squared plus ((18 minus 18 multiply by sinus of (3.14 multiply by x multiply by 40 divide by 1000000)) divide by (4 multiply by 3.14 multiply by x)) squared )
  • square root of (((twelve multiply by sinus of (three . fourteen multiply by x multiply by twenty divide by one million) minus six multiply by sinus of (three . fourteen multiply by x multiply by forty divide by one million)) divide by (four multiply by three . fourteen multiply by x)) to the power of two plus ((eighteen minus eighteen multiply by sinus of (three . fourteen multiply by x multiply by forty divide by one million)) divide by (four multiply by three . fourteen multiply by x)) to the power of two)
  • √(((12*sin(3.14*x*20/1000000)-6*sin(3.14*x*40/1000000))/(4*3.14*x))^2+((18-18*sin(3.14*x*40/1000000))/(4*3.14*x))^2)
  • sqrt(((12*sin(3.14*x*20/1000000)-6*sin(3.14*x*40/1000000))/(4*3.14*x))2+((18-18*sin(3.14*x*40/1000000))/(4*3.14*x))2)
  • sqrt12*sin3.14*x*20/1000000-6*sin3.14*x*40/1000000/4*3.14*x2+18-18*sin3.14*x*40/1000000/4*3.14*x2
  • sqrt(((12*sin(3.14*x*20/1000000)-6*sin(3.14*x*40/1000000))/(4*3.14*x))²+((18-18*sin(3.14*x*40/1000000))/(4*3.14*x))²)
  • sqrt(((12*sin(3.14*x*20/1000000)-6*sin(3.14*x*40/1000000))/(4*3.14*x)) to the power of 2+((18-18*sin(3.14*x*40/1000000))/(4*3.14*x)) to the power of 2)
  • sqrt(((12sin(3.14x20/1000000)-6sin(3.14x40/1000000))/(43.14x))^2+((18-18sin(3.14x40/1000000))/(43.14x))^2)
  • sqrt(((12sin(3.14x20/1000000)-6sin(3.14x40/1000000))/(43.14x))2+((18-18sin(3.14x40/1000000))/(43.14x))2)
  • sqrt12sin3.14x20/1000000-6sin3.14x40/1000000/43.14x2+18-18sin3.14x40/1000000/43.14x2
  • sqrt12sin3.14x20/1000000-6sin3.14x40/1000000/43.14x^2+18-18sin3.14x40/1000000/43.14x^2
  • sqrt(((12*sin(3.14*x*20 divide by 1000000)-6*sin(3.14*x*40 divide by 1000000)) divide by (4*3.14*x))^2+((18-18*sin(3.14*x*40 divide by 1000000)) divide by (4*3.14*x))^2)

  • Similar expressions

  • sqrt(((12*sin(3.14*x*20/1000000)-6*sin(3.14*x*40/1000000))/(4*3.14*x))^2-((18-18*sin(3.14*x*40/1000000))/(4*3.14*x))^2)
  • sqrt(((12*sin(3.14*x*20/1000000)-6*sin(3.14*x*40/1000000))/(4*3.14*x))^2+((18+18*sin(3.14*x*40/1000000))/(4*3.14*x))^2)
  • sqrt(((12*sin(3.14*x*20/1000000)+6*sin(3.14*x*40/1000000))/(4*3.14*x))^2+((18-18*sin(3.14*x*40/1000000))/(4*3.14*x))^2)
Plotting a function graph/ sqrt(((12*sin(3.14*x*20/1000000)-6*sin(3.14*x*40/1000000))/(4*3.14*x))^2+((18-18*sin(3.14*x*40/1000000))/(4*3.14*x))^2)

Graphing y = sqrt(((12*sin(3.14*x*20/1000000)-6*sin(3.14*x*40/1000000))/(4*3.14*x))^2+((18-18*sin(3.14*x*40/1000000))/(4*3.14*x))^2)

v

The graph:

from to

Intersection points:

does show?

Piecewise:

The solution

You have entered [src] 
                  _______________________________________________________________
                 /                                   2                         2 
                /  /      //157*x\\        //157*x\\\    /           //157*x\\\  
               /   |      ||-----||        ||-----|||    |           ||-----|||  
              /    |      |\  50 /|        |\  50 /||    |           |\  50 /||  
             /     |12*sin|-------| - 6*sin|-------||    |18 - 18*sin|-------||  
            /      |      \ 50000 /        \ 25000 /|    |           \ 25000 /|  
f(x) =     /       |--------------------------------|  + |--------------------|  
          /        |            157*4               |    |      157*4         |  
         /         |            -----*x             |    |      -----*x       |  
       \/          \              50                /    \        50          /
$$f{\left(x \right)} = \sqrt{\left(\frac{18 - 18 \sin{\left(\frac{\frac{157}{50} x}{25000} \right)}}{\frac{4 \cdot 157}{50} x}\right)^{2} + \left(\frac{12 \sin{\left(\frac{\frac{157}{50} x}{50000} \right)} - 6 \sin{\left(\frac{\frac{157}{50} x}{25000} \right)}}{\frac{4 \cdot 157}{50} x}\right)^{2}}$$ 
f = sqrt(((18 - 18*sin((157*x/50)/25000))/(((157*4/50)*x)))^2 + ((12*sin((157*x/50)/50000) - 6*sin((157*x/50)/25000))/(((157*4/50)*x)))^2)
The graph of the function
The domain of the function
The points at which the function is not precisely defined:
$$x_{1} = 0$$
The points of intersection with the Y axis coordinate
The graph crosses Y axis when x equals 0:
substitute x = 0 to sqrt(((12*sin((157*x/50)/50000) - 6*sin((157*x/50)/25000))/(((157*4/50)*x)))^2 + ((18 - 18*sin((157*x/50)/25000))/(((157*4/50)*x)))^2).
$$\sqrt{\left(\frac{12 \sin{\left(\frac{0 \frac{157}{50}}{50000} \right)} - 6 \sin{\left(\frac{0 \frac{157}{50}}{25000} \right)}}{0 \frac{4 \cdot 157}{50}}\right)^{2} + \left(\frac{18 - 18 \sin{\left(\frac{0 \frac{157}{50}}{25000} \right)}}{0 \frac{4 \cdot 157}{50}}\right)^{2}}$$
The result:
$$f{\left(0 \right)} = \text{NaN}$$
- the solutions of the equation d'not exist
Vertical asymptotes
Have:
$$x_{1} = 0$$
Horizontal asymptotes
Let’s find horizontal asymptotes with help of the limits of this function at x->+oo and x->-oo
$$\lim_{x \to -\infty} \sqrt{\left(\frac{18 - 18 \sin{\left(\frac{\frac{157}{50} x}{25000} \right)}}{\frac{4 \cdot 157}{50} x}\right)^{2} + \left(\frac{12 \sin{\left(\frac{\frac{157}{50} x}{50000} \right)} - 6 \sin{\left(\frac{\frac{157}{50} x}{25000} \right)}}{\frac{4 \cdot 157}{50} x}\right)^{2}} = 0$$
Let's take the limit
so,
equation of the horizontal asymptote on the left:
$$y = 0$$
$$\lim_{x \to \infty} \sqrt{\left(\frac{18 - 18 \sin{\left(\frac{\frac{157}{50} x}{25000} \right)}}{\frac{4 \cdot 157}{50} x}\right)^{2} + \left(\frac{12 \sin{\left(\frac{\frac{157}{50} x}{50000} \right)} - 6 \sin{\left(\frac{\frac{157}{50} x}{25000} \right)}}{\frac{4 \cdot 157}{50} x}\right)^{2}} = 0$$
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 sqrt(((12*sin((157*x/50)/50000) - 6*sin((157*x/50)/25000))/(((157*4/50)*x)))^2 + ((18 - 18*sin((157*x/50)/25000))/(((157*4/50)*x)))^2), divided by x at x->+oo and x ->-oo
$$\lim_{x \to -\infty}\left(\frac{\sqrt{\left(\frac{18 - 18 \sin{\left(\frac{\frac{157}{50} x}{25000} \right)}}{\frac{4 \cdot 157}{50} x}\right)^{2} + \left(\frac{12 \sin{\left(\frac{\frac{157}{50} x}{50000} \right)} - 6 \sin{\left(\frac{\frac{157}{50} x}{25000} \right)}}{\frac{4 \cdot 157}{50} x}\right)^{2}}}{x}\right) = 0$$
Let's take the limit
so,
inclined coincides with the horizontal asymptote on the right
$$\lim_{x \to \infty}\left(\frac{\sqrt{\left(\frac{18 - 18 \sin{\left(\frac{\frac{157}{50} x}{25000} \right)}}{\frac{4 \cdot 157}{50} x}\right)^{2} + \left(\frac{12 \sin{\left(\frac{\frac{157}{50} x}{50000} \right)} - 6 \sin{\left(\frac{\frac{157}{50} x}{25000} \right)}}{\frac{4 \cdot 157}{50} x}\right)^{2}}}{x}\right) = 0$$
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:
$$\sqrt{\left(\frac{18 - 18 \sin{\left(\frac{\frac{157}{50} x}{25000} \right)}}{\frac{4 \cdot 157}{50} x}\right)^{2} + \left(\frac{12 \sin{\left(\frac{\frac{157}{50} x}{50000} \right)} - 6 \sin{\left(\frac{\frac{157}{50} x}{25000} \right)}}{\frac{4 \cdot 157}{50} x}\right)^{2}} = \sqrt{\frac{625 \left(- 12 \sin{\left(\frac{157 x}{2500000} \right)} + 6 \sin{\left(\frac{157 x}{1250000} \right)}\right)^{2}}{98596 x^{2}} + \frac{625 \left(18 \sin{\left(\frac{157 x}{1250000} \right)} + 18\right)^{2}}{98596 x^{2}}}$$
- No
$$\sqrt{\left(\frac{18 - 18 \sin{\left(\frac{\frac{157}{50} x}{25000} \right)}}{\frac{4 \cdot 157}{50} x}\right)^{2} + \left(\frac{12 \sin{\left(\frac{\frac{157}{50} x}{50000} \right)} - 6 \sin{\left(\frac{\frac{157}{50} x}{25000} \right)}}{\frac{4 \cdot 157}{50} x}\right)^{2}} = - \sqrt{\frac{625 \left(- 12 \sin{\left(\frac{157 x}{2500000} \right)} + 6 \sin{\left(\frac{157 x}{1250000} \right)}\right)^{2}}{98596 x^{2}} + \frac{625 \left(18 \sin{\left(\frac{157 x}{1250000} \right)} + 18\right)^{2}}{98596 x^{2}}}$$
- No
so, the function
not is
neither even, nor odd
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