Mister Exam

Other calculators

  • How to use it?

  • Graphing y =:
  • -x^3-3x^2+3
  • -x^3+3x^2-2
  • x^3-12x+3
  • x^2+4x+4

  • Identical expressions

  • arcsinx/(x^(three / four))
  • arc sinus of x divide by (x to the power of (3 divide by 4))
  • arc sinus of x divide by (x to the power of (three divide by four))
  • arcsinx/(x(3/4))
  • arcsinx/x3/4
  • arcsinx/x^3/4
  • arcsinx divide by (x^(3 divide by 4))
Plotting a function graph/ arcsinx/(x^(3/4))

Graphing y = arcsinx/(x^(3/4))

v

The graph:

from to

Intersection points:

does show?

Piecewise:

The solution

You have entered [src] 
       asin(x)
f(x) = -------
          3/4 
         x
f(x)=asin⁡(x)x34f{\left(x \right)} = \frac{\operatorname{asin}{\left(x \right)}}{x^{\frac{3}{4}}} 
f = asin(x)/x^(3/4)
The graph of the function
02468-8-6-4-2-10100.02.0
The domain of the function
The points at which the function is not precisely defined:
x1=0x_{1} = 0
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:
asin⁡(x)x34=0\frac{\operatorname{asin}{\left(x \right)}}{x^{\frac{3}{4}}} = 0
Solve this equation
Solution is not found,
it's possible that the graph doesn't intersect the axis X
The points of intersection with the Y axis coordinate
The graph crosses Y axis when x equals 0:
substitute x = 0 to asin(x)/x^(3/4).
asin⁡(0)034\frac{\operatorname{asin}{\left(0 \right)}}{0^{\frac{3}{4}}}
The result:
f(0)=NaNf{\left(0 \right)} = \text{NaN}
- the solutions of the equation d'not exist
Extrema of the function
In order to find the extrema, we need to solve the equation
ddxf(x)=0\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:
ddxf(x)=\frac{d}{d x} f{\left(x \right)} =
the first derivative
1x341−x2−3asin⁡(x)4x74=0\frac{1}{x^{\frac{3}{4}} \sqrt{1 - x^{2}}} - \frac{3 \operatorname{asin}{\left(x \right)}}{4 x^{\frac{7}{4}}} = 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
d2dx2f(x)=0\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:
d2dx2f(x)=\frac{d^{2}}{d x^{2}} f{\left(x \right)} =
the second derivative
x4(1−x2)32−32x741−x2+21asin⁡(x)16x114=0\frac{\sqrt[4]{x}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{3}{2 x^{\frac{7}{4}} \sqrt{1 - x^{2}}} + \frac{21 \operatorname{asin}{\left(x \right)}}{16 x^{\frac{11}{4}}} = 0
Solve this equation
Solutions are not found,
maybe, the function has no inflections
Vertical asymptotes
Have:
x1=0x_{1} = 0
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→−∞(asin⁡(x)x34)y = \lim_{x \to -\infty}\left(\frac{\operatorname{asin}{\left(x \right)}}{x^{\frac{3}{4}}}\right)
True

Let's take the limit
so,
equation of the horizontal asymptote on the right:
y=lim⁡x→∞(asin⁡(x)x34)y = \lim_{x \to \infty}\left(\frac{\operatorname{asin}{\left(x \right)}}{x^{\frac{3}{4}}}\right)
Inclined asymptotes
Inclined asymptote can be found by calculating the limit of asin(x)/x^(3/4), divided by x at x->+oo and x ->-oo
True

Let's take the limit
so,
inclined asymptote equation on the left:
y=xlim⁡x→−∞(asin⁡(x)x34x)y = x \lim_{x \to -\infty}\left(\frac{\operatorname{asin}{\left(x \right)}}{x^{\frac{3}{4}} x}\right)
True

Let's take the limit
so,
inclined asymptote equation on the right:
y=xlim⁡x→∞(asin⁡(x)x34x)y = x \lim_{x \to \infty}\left(\frac{\operatorname{asin}{\left(x \right)}}{x^{\frac{3}{4}} 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:
asin⁡(x)x34=−asin⁡(x)(−x)34\frac{\operatorname{asin}{\left(x \right)}}{x^{\frac{3}{4}}} = - \frac{\operatorname{asin}{\left(x \right)}}{\left(- x\right)^{\frac{3}{4}}}
- No
asin⁡(x)x34=asin⁡(x)(−x)34\frac{\operatorname{asin}{\left(x \right)}}{x^{\frac{3}{4}}} = \frac{\operatorname{asin}{\left(x \right)}}{\left(- x\right)^{\frac{3}{4}}}
- No
so, the function
not is
neither even, nor odd
    © Mister Exam – Calculator