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  • Identical expressions

  • (cot(sqrt(x)))^cos(x)
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  • (cot(sqrt(x)))cos(x)
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  • Similar expressions

  • (cot(sqrt(x)))^cosx
Plotting a function graph/ (cot(sqrt(x)))^cos(x)

Graphing y = (cot(sqrt(x)))^cos(x)

v

The graph:

from to

Intersection points:

does show?

Piecewise:

The solution

You have entered [src] 
          cos(x)/  ___\
f(x) = cot      \\/ x /
f(x)=cot⁡cos⁡(x)(x)f{\left(x \right)} = \cot^{\cos{\left(x \right)}}{\left(\sqrt{x} \right)} 
f = cot(sqrt(x))^cos(x)
The graph of the function
02468-8-6-4-2-10100200
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:
cot⁡cos⁡(x)(x)=0\cot^{\cos{\left(x \right)}}{\left(\sqrt{x} \right)} = 0
Solve this equation
The points of intersection with the axis X:

Numerical solution
x1=9.86960440108936x_{1} = 9.86960440108936
The points of intersection with the Y axis coordinate
The graph crosses Y axis when x equals 0:
substitute x = 0 to cot(sqrt(x))^cos(x).
cot⁡cos⁡(0)(0)\cot^{\cos{\left(0 \right)}}{\left(\sqrt{0} \right)}
The result:
f(0)=∞~f{\left(0 \right)} = \tilde{\infty}
sof doesn't intersect Y
Horizontal asymptotes
Let’s find horizontal asymptotes with help of the limits of this function at x->+oo and x->-oo
lim⁡x→−∞cot⁡cos⁡(x)(x)=(−i)⟨−1,1⟩\lim_{x \to -\infty} \cot^{\cos{\left(x \right)}}{\left(\sqrt{x} \right)} = \left(- i\right)^{\left\langle -1, 1\right\rangle}
Let's take the limit
so,
equation of the horizontal asymptote on the left:
y=(−i)⟨−1,1⟩y = \left(- i\right)^{\left\langle -1, 1\right\rangle}
True

Let's take the limit
so,
equation of the horizontal asymptote on the right:
y=lim⁡x→∞cot⁡cos⁡(x)(x)y = \lim_{x \to \infty} \cot^{\cos{\left(x \right)}}{\left(\sqrt{x} \right)}
Inclined asymptotes
Inclined asymptote can be found by calculating the limit of cot(sqrt(x))^cos(x), divided by x at x->+oo and x ->-oo
lim⁡x→−∞(cot⁡cos⁡(x)(x)x)=0\lim_{x \to -\infty}\left(\frac{\cot^{\cos{\left(x \right)}}{\left(\sqrt{x} \right)}}{x}\right) = 0
Let's take the limit
so,
inclined coincides with the horizontal asymptote on the right
True

Let's take the limit
so,
inclined asymptote equation on the right:
y=xlim⁡x→∞(cot⁡cos⁡(x)(x)x)y = x \lim_{x \to \infty}\left(\frac{\cot^{\cos{\left(x \right)}}{\left(\sqrt{x} \right)}}{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:
cot⁡cos⁡(x)(x)=cot⁡cos⁡(x)(−x)\cot^{\cos{\left(x \right)}}{\left(\sqrt{x} \right)} = \cot^{\cos{\left(x \right)}}{\left(\sqrt{- x} \right)}
- No
cot⁡cos⁡(x)(x)=−cot⁡cos⁡(x)(−x)\cot^{\cos{\left(x \right)}}{\left(\sqrt{x} \right)} = - \cot^{\cos{\left(x \right)}}{\left(\sqrt{- x} \right)}
- No
so, the function
not is
neither even, nor odd
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