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  • Graphing y =:
  • x^2*sqrt(1+x)
  • (x^2-6x+13)/(x-3)
  • -x^2+3x-2
  • (x+2)^2-3

  • Identical expressions

  • (sqrt(three)*cot(x+pi/ three))^(two /(five *x^ three - seven *x^ four))
  • ( square root of (3) multiply by cotangent of (x plus Pi divide by 3)) to the power of (2 divide by (5 multiply by x cubed minus 7 multiply by x to the power of 4))
  • ( square root of (three) multiply by cotangent of (x plus Pi divide by three)) to the power of (two divide by (five multiply by x to the power of three minus seven multiply by x to the power of four))
  • (√(3)*cot(x+pi/3))^(2/(5*x^3-7*x^4))
  • (sqrt(3)*cot(x+pi/3))(2/(5*x3-7*x4))
  • sqrt3*cotx+pi/32/5*x3-7*x4
  • (sqrt(3)*cot(x+pi/3))^(2/(5*x³-7*x⁴))
  • (sqrt(3)*cot(x+pi/3)) to the power of (2/(5*x to the power of 3-7*x to the power of 4))
  • (sqrt(3)cot(x+pi/3))^(2/(5x^3-7x^4))
  • (sqrt(3)cot(x+pi/3))(2/(5x3-7x4))
  • sqrt3cotx+pi/32/5x3-7x4
  • sqrt3cotx+pi/3^2/5x^3-7x^4
  • (sqrt(3)*cot(x+pi divide by 3))^(2 divide by (5*x^3-7*x^4))

  • Similar expressions

  • (sqrt(3)*cot(x+pi/3))^(2/(5*x^3+7*x^4))
  • (sqrt(3)*cot(x-pi/3))^(2/(5*x^3-7*x^4))
Plotting a function graph/ (sqrt(3)*cot(x+pi/3))^(2/(5*x^3-7*x^4))

Graphing y = (sqrt(3)*cot(x+pi/3))^(2/(5*x^3-7*x^4))

v

The graph:

from to

Intersection points:

does show?

Piecewise:

The solution

You have entered [src] 
                               2     
                          -----------
                             3      4
                          5*x  - 7*x 
       /  ___    /    pi\\           
f(x) = |\/ 3 *cot|x + --||           
       \         \    3 //
$$f{\left(x \right)} = \left(\sqrt{3} \cot{\left(x + \frac{\pi}{3} \right)}\right)^{\frac{2}{- 7 x^{4} + 5 x^{3}}}$$ 
f = (sqrt(3)*cot(x + pi/3))^(2/(-7*x^4 + 5*x^3))
The graph of the function
The domain of the function
The points at which the function is not precisely defined:
$$x_{1} = 0$$
$$x_{2} = 0.714285714285714$$
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:
$$\left(\sqrt{3} \cot{\left(x + \frac{\pi}{3} \right)}\right)^{\frac{2}{- 7 x^{4} + 5 x^{3}}} = 0$$
Solve this equation
The points of intersection with the axis X:

Analytical solution
$$x_{1} = \frac{\pi}{6}$$
Numerical solution
$$x_{1} = 0.523598775598299$$
The points of intersection with the Y axis coordinate
The graph crosses Y axis when x equals 0:
substitute x = 0 to (sqrt(3)*cot(x + pi/3))^(2/(5*x^3 - 7*x^4)).
$$\left(\sqrt{3} \cot{\left(\frac{\pi}{3} \right)}\right)^{\frac{2}{5 \cdot 0^{3} - 7 \cdot 0^{4}}}$$
The result:
$$f{\left(0 \right)} = \text{NaN}$$
- the solutions of the equation d'not exist
Vertical asymptotes
Have:
$$x_{1} = 0$$
$$x_{2} = 0.714285714285714$$
Horizontal asymptotes
Let’s find horizontal asymptotes with help of the limits of this function at x->+oo and x->-oo
True

Let's take the limit
so,
equation of the horizontal asymptote on the left:
$$y = \lim_{x \to -\infty} \left(\sqrt{3} \cot{\left(x + \frac{\pi}{3} \right)}\right)^{\frac{2}{- 7 x^{4} + 5 x^{3}}}$$
True

Let's take the limit
so,
equation of the horizontal asymptote on the right:
$$y = \lim_{x \to \infty} \left(\sqrt{3} \cot{\left(x + \frac{\pi}{3} \right)}\right)^{\frac{2}{- 7 x^{4} + 5 x^{3}}}$$
Inclined asymptotes
Inclined asymptote can be found by calculating the limit of (sqrt(3)*cot(x + pi/3))^(2/(5*x^3 - 7*x^4)), divided by x at x->+oo and x ->-oo
True

Let's take the limit
so,
inclined asymptote equation on the left:
$$y = x \lim_{x \to -\infty}\left(\frac{\left(\sqrt{3} \cot{\left(x + \frac{\pi}{3} \right)}\right)^{\frac{2}{- 7 x^{4} + 5 x^{3}}}}{x}\right)$$
True

Let's take the limit
so,
inclined asymptote equation on the right:
$$y = x \lim_{x \to \infty}\left(\frac{\left(\sqrt{3} \cot{\left(x + \frac{\pi}{3} \right)}\right)^{\frac{2}{- 7 x^{4} + 5 x^{3}}}}{x}\right)$$
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:
$$\left(\sqrt{3} \cot{\left(x + \frac{\pi}{3} \right)}\right)^{\frac{2}{- 7 x^{4} + 5 x^{3}}} = \left(- \sqrt{3} \cot{\left(x - \frac{\pi}{3} \right)}\right)^{\frac{2}{- 7 x^{4} - 5 x^{3}}}$$
- No
$$\left(\sqrt{3} \cot{\left(x + \frac{\pi}{3} \right)}\right)^{\frac{2}{- 7 x^{4} + 5 x^{3}}} = - \left(- \sqrt{3} \cot{\left(x - \frac{\pi}{3} \right)}\right)^{\frac{2}{- 7 x^{4} - 5 x^{3}}}$$
- No
so, the function
not is
neither even, nor odd
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