Mister Exam
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-
How to use it?
- Graphing y =:
- x/(4+x^2)
- (x+1)*e^(2*x)
- (x-1)^3/(x-2)^2
- (x-1)^2*(x+5)
- Derivative of:
-
asin(e^(3*x))
-
Identical expressions
- asin(e^(three *x))
- arc sinus of e of (e to the power of (3 multiply by x))
- arc sinus of e of (e to the power of (three multiply by x))
- asin(e(3*x))
- asine3*x
- asin(e^(3x))
- asin(e(3x))
- asine3x
- asine^3x
-
Similar expressions
- arcsin(e^(3*x))
Graphing y = asin(e^(3*x))
The solution
You have entered
[src]
/ 3*x\ f(x) = asin\E /
$$f{\left(x \right)} = \operatorname{asin}{\left(e^{3 x} \right)}$$
f = asin(E^(3*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:
$$\operatorname{asin}{\left(e^{3 x} \right)} = 0$$
Solve this equation
The points of intersection with the axis X:
Numerical solution
$$x_{1} = -24.8676436671489$$
$$x_{2} = -22.8676436671489$$
$$x_{3} = -58.8676436671489$$
$$x_{4} = -98.8676436671489$$
$$x_{5} = -60.8676436671489$$
$$x_{6} = -86.8676436671489$$
$$x_{7} = -78.8676436671489$$
$$x_{8} = -106.867643667149$$
$$x_{9} = -48.8676436671489$$
$$x_{10} = -20.8676436671489$$
$$x_{11} = -18.8676436671489$$
$$x_{12} = -52.8676436671489$$
$$x_{13} = -70.8676436671489$$
$$x_{14} = -10.867643667137$$
$$x_{15} = -12.8676436671489$$
$$x_{16} = -94.8676436671489$$
$$x_{17} = -44.8676436671489$$
$$x_{18} = -30.8676436671489$$
$$x_{19} = -34.8676436671489$$
$$x_{20} = -40.8676436671489$$
$$x_{21} = -46.8676436671489$$
$$x_{22} = -104.867643667149$$
$$x_{23} = -62.8676436671489$$
$$x_{24} = -66.8676436671489$$
$$x_{25} = -74.8676436671489$$
$$x_{26} = -84.8676436671489$$
$$x_{27} = -64.8676436671489$$
$$x_{28} = -100.867643667149$$
$$x_{29} = -50.8676436671489$$
$$x_{30} = -92.8676436671489$$
$$x_{31} = -68.8676436671489$$
$$x_{32} = -32.8676436671489$$
$$x_{33} = -26.8676436671489$$
$$x_{34} = -102.867643667149$$
$$x_{35} = -56.8676436671489$$
$$x_{36} = -82.8676436671489$$
$$x_{37} = -16.8676436671489$$
$$x_{38} = -36.8676436671489$$
$$x_{39} = -88.8676436671489$$
$$x_{40} = -90.8676436671489$$
$$x_{41} = -80.8676436671489$$
$$x_{42} = -72.8676436671489$$
$$x_{43} = -42.8676436671489$$
$$x_{44} = -54.8676436671489$$
$$x_{45} = -76.8676436671489$$
$$x_{46} = -38.8676436671489$$
$$x_{47} = -28.8676436671489$$
$$x_{48} = -14.8676436671489$$
$$x_{49} = -96.8676436671489$$
so we need to solve the equation:
$$\operatorname{asin}{\left(e^{3 x} \right)} = 0$$
Solve this equation
The points of intersection with the axis X:
Numerical solution
$$x_{1} = -24.8676436671489$$
$$x_{2} = -22.8676436671489$$
$$x_{3} = -58.8676436671489$$
$$x_{4} = -98.8676436671489$$
$$x_{5} = -60.8676436671489$$
$$x_{6} = -86.8676436671489$$
$$x_{7} = -78.8676436671489$$
$$x_{8} = -106.867643667149$$
$$x_{9} = -48.8676436671489$$
$$x_{10} = -20.8676436671489$$
$$x_{11} = -18.8676436671489$$
$$x_{12} = -52.8676436671489$$
$$x_{13} = -70.8676436671489$$
$$x_{14} = -10.867643667137$$
$$x_{15} = -12.8676436671489$$
$$x_{16} = -94.8676436671489$$
$$x_{17} = -44.8676436671489$$
$$x_{18} = -30.8676436671489$$
$$x_{19} = -34.8676436671489$$
$$x_{20} = -40.8676436671489$$
$$x_{21} = -46.8676436671489$$
$$x_{22} = -104.867643667149$$
$$x_{23} = -62.8676436671489$$
$$x_{24} = -66.8676436671489$$
$$x_{25} = -74.8676436671489$$
$$x_{26} = -84.8676436671489$$
$$x_{27} = -64.8676436671489$$
$$x_{28} = -100.867643667149$$
$$x_{29} = -50.8676436671489$$
$$x_{30} = -92.8676436671489$$
$$x_{31} = -68.8676436671489$$
$$x_{32} = -32.8676436671489$$
$$x_{33} = -26.8676436671489$$
$$x_{34} = -102.867643667149$$
$$x_{35} = -56.8676436671489$$
$$x_{36} = -82.8676436671489$$
$$x_{37} = -16.8676436671489$$
$$x_{38} = -36.8676436671489$$
$$x_{39} = -88.8676436671489$$
$$x_{40} = -90.8676436671489$$
$$x_{41} = -80.8676436671489$$
$$x_{42} = -72.8676436671489$$
$$x_{43} = -42.8676436671489$$
$$x_{44} = -54.8676436671489$$
$$x_{45} = -76.8676436671489$$
$$x_{46} = -38.8676436671489$$
$$x_{47} = -28.8676436671489$$
$$x_{48} = -14.8676436671489$$
$$x_{49} = -96.8676436671489$$
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
$$\frac{3 e^{3 x}}{\sqrt{1 - e^{6 x}}} = 0$$
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
$$\frac{3 e^{3 x}}{\sqrt{1 - e^{6 x}}} = 0$$
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
$$\frac{9 \left(1 + \frac{e^{6 x}}{1 - e^{6 x}}\right) e^{3 x}}{\sqrt{1 - e^{6 x}}} = 0$$
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
$$\frac{9 \left(1 + \frac{e^{6 x}}{1 - e^{6 x}}\right) e^{3 x}}{\sqrt{1 - e^{6 x}}} = 0$$
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
$$\lim_{x \to -\infty} \operatorname{asin}{\left(e^{3 x} \right)} = 0$$
Let's take the limit
so,
equation of the horizontal asymptote on the left:
$$y = 0$$
$$\lim_{x \to \infty} \operatorname{asin}{\left(e^{3 x} \right)} = - \infty i$$
Let's take the limit
so,
horizontal asymptote on the right doesn’t exist
$$\lim_{x \to -\infty} \operatorname{asin}{\left(e^{3 x} \right)} = 0$$
Let's take the limit
so,
equation of the horizontal asymptote on the left:
$$y = 0$$
$$\lim_{x \to \infty} \operatorname{asin}{\left(e^{3 x} \right)} = - \infty i$$
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 asin(E^(3*x)), divided by x at x->+oo and x ->-oo
$$\lim_{x \to -\infty}\left(\frac{\operatorname{asin}{\left(e^{3 x} \right)}}{x}\right) = 0$$
Let's take the limit
so,
inclined coincides with the horizontal asymptote on the right
Let's take the limit
so,
inclined asymptote equation on the right:
$$y = x \lim_{x \to \infty}\left(\frac{\operatorname{asin}{\left(e^{3 x} \right)}}{x}\right)$$
$$\lim_{x \to -\infty}\left(\frac{\operatorname{asin}{\left(e^{3 x} \right)}}{x}\right) = 0$$
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:
$$y = x \lim_{x \to \infty}\left(\frac{\operatorname{asin}{\left(e^{3 x} \right)}}{x}\right)$$
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:
$$\operatorname{asin}{\left(e^{3 x} \right)} = \operatorname{asin}{\left(e^{- 3 x} \right)}$$
- No
$$\operatorname{asin}{\left(e^{3 x} \right)} = - \operatorname{asin}{\left(e^{- 3 x} \right)}$$
- No
so, the function
not is
neither even, nor odd
So, check:
$$\operatorname{asin}{\left(e^{3 x} \right)} = \operatorname{asin}{\left(e^{- 3 x} \right)}$$
- No
$$\operatorname{asin}{\left(e^{3 x} \right)} = - \operatorname{asin}{\left(e^{- 3 x} \right)}$$
- No
so, the function
not is
neither even, nor odd