Mister Exam
Other calculators
- Graph of implicit function
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- Integral Step by Step
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- Graph in Polar Coordinates
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- Curve in 3D space defined parametrically
- Area between lines
- The intersection points of functions
-
How to use it?
- Graphing y =:
- -x^2+2x+4
- -x^2+2x-3
- -x^2+4x-2
- (x^2-2)/x
- Derivative of:
-
x^(sin(x))
-
Identical expressions
- x^(sin(x))
- x to the power of ( sinus of (x))
- x(sin(x))
- xsinx
- x^sinx
-
Similar expressions
- x^(sinx)
Graphing y = x^(sin(x))
The solution
You have entered
[src]
sin(x) f(x) = x
$$f{\left(x \right)} = x^{\sin{\left(x \right)}}$$
f = x^sin(x)
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:
$$x^{\sin{\left(x \right)}} = 0$$
Solve this equation
Solution is not found,
it's possible that the graph doesn't intersect the axis X
so we need to solve the equation:
$$x^{\sin{\left(x \right)}} = 0$$
Solve this equation
Solution is not found,
it's possible that the graph doesn't intersect the axis X
Horizontal asymptotes
Let’s find horizontal asymptotes with help of the limits of this function at x->+oo and x->-oo
$$\lim_{x \to -\infty} x^{\sin{\left(x \right)}} = \left(-\infty\right)^{\left\langle -1, 1\right\rangle}$$
Let's take the limit
so,
equation of the horizontal asymptote on the left:
$$y = \left(-\infty\right)^{\left\langle -1, 1\right\rangle}$$
$$\lim_{x \to \infty} x^{\sin{\left(x \right)}} = \infty^{\left\langle -1, 1\right\rangle}$$
Let's take the limit
so,
equation of the horizontal asymptote on the right:
$$y = \infty^{\left\langle -1, 1\right\rangle}$$
$$\lim_{x \to -\infty} x^{\sin{\left(x \right)}} = \left(-\infty\right)^{\left\langle -1, 1\right\rangle}$$
Let's take the limit
so,
equation of the horizontal asymptote on the left:
$$y = \left(-\infty\right)^{\left\langle -1, 1\right\rangle}$$
$$\lim_{x \to \infty} x^{\sin{\left(x \right)}} = \infty^{\left\langle -1, 1\right\rangle}$$
Let's take the limit
so,
equation of the horizontal asymptote on the right:
$$y = \infty^{\left\langle -1, 1\right\rangle}$$
Inclined asymptotes
Inclined asymptote can be found by calculating the limit of x^sin(x), divided by x at x->+oo and x ->-oo
$$\lim_{x \to -\infty}\left(\frac{x^{\sin{\left(x \right)}}}{x}\right) = \left(-\infty\right)^{\left\langle -2, 0\right\rangle}$$
Let's take the limit
so,
inclined asymptote equation on the left:
$$y = \left(-\infty\right)^{\left\langle -2, 0\right\rangle} x$$
$$\lim_{x \to \infty}\left(\frac{x^{\sin{\left(x \right)}}}{x}\right) = \infty^{\left\langle -2, 0\right\rangle}$$
Let's take the limit
so,
inclined asymptote equation on the right:
$$y = \infty^{\left\langle -2, 0\right\rangle} x$$
$$\lim_{x \to -\infty}\left(\frac{x^{\sin{\left(x \right)}}}{x}\right) = \left(-\infty\right)^{\left\langle -2, 0\right\rangle}$$
Let's take the limit
so,
inclined asymptote equation on the left:
$$y = \left(-\infty\right)^{\left\langle -2, 0\right\rangle} x$$
$$\lim_{x \to \infty}\left(\frac{x^{\sin{\left(x \right)}}}{x}\right) = \infty^{\left\langle -2, 0\right\rangle}$$
Let's take the limit
so,
inclined asymptote equation on the right:
$$y = \infty^{\left\langle -2, 0\right\rangle} x$$
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:
$$x^{\sin{\left(x \right)}} = \left(- x\right)^{- \sin{\left(x \right)}}$$
- No
$$x^{\sin{\left(x \right)}} = - \left(- x\right)^{- \sin{\left(x \right)}}$$
- No
so, the function
not is
neither even, nor odd
So, check:
$$x^{\sin{\left(x \right)}} = \left(- x\right)^{- \sin{\left(x \right)}}$$
- No
$$x^{\sin{\left(x \right)}} = - \left(- x\right)^{- \sin{\left(x \right)}}$$
- No
so, the function
not is
neither even, nor odd
The graph