Mister Exam

Other calculators

  • How to use it?

  • Graphing y =:
  • x^3+3x^2-9x+15
  • -x^2+6x-8
  • x^2-2x-8
  • x^2-2lnx

  • Identical expressions

  • seven *log(x)*atan(x)
  • 7 multiply by logarithm of (x) multiply by arc tangent of gent of (x)
  • seven multiply by logarithm of (x) multiply by arc tangent of gent of (x)
  • 7log(x)atan(x)
  • 7logxatanx

  • Similar expressions

  • 7*log(x)*arctan(x)
  • 7*log(x)*arctanx
Plotting a function graph/ 7*log(x)*atan(x)

Graphing y = 7*log(x)*atan(x)

v

The graph:

from to

Intersection points:

does show?

Piecewise:

The solution

You have entered [src] 
f(x) = 7*log(x)*atan(x)
f(x)=7log⁡(x)atan⁡(x)f{\left(x \right)} = 7 \log{\left(x \right)} \operatorname{atan}{\left(x \right)} 
f = (7*log(x))*atan(x)
The graph of the function
02468-8-6-4-2-1010-2525
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:
7log⁡(x)atan⁡(x)=07 \log{\left(x \right)} \operatorname{atan}{\left(x \right)} = 0
Solve this equation
The points of intersection with the axis X:

Analytical solution
x1=1x_{1} = 1
Numerical solution
x1=1x_{1} = 1
The points of intersection with the Y axis coordinate
The graph crosses Y axis when x equals 0:
substitute x = 0 to (7*log(x))*atan(x).
7log⁡(0)atan⁡(0)7 \log{\left(0 \right)} \operatorname{atan}{\left(0 \right)}
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
7log⁡(x)x2+1+7atan⁡(x)x=0\frac{7 \log{\left(x \right)}}{x^{2} + 1} + \frac{7 \operatorname{atan}{\left(x \right)}}{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
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
7(−2xlog⁡(x)(x2+1)2+2x(x2+1)−atan⁡(x)x2)=07 \left(- \frac{2 x \log{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{2}{x \left(x^{2} + 1\right)} - \frac{\operatorname{atan}{\left(x \right)}}{x^{2}}\right) = 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→−∞(7log⁡(x)atan⁡(x))=−∞\lim_{x \to -\infty}\left(7 \log{\left(x \right)} \operatorname{atan}{\left(x \right)}\right) = -\infty
Let's take the limit
so,
horizontal asymptote on the left doesn’t exist
lim⁡x→∞(7log⁡(x)atan⁡(x))=∞\lim_{x \to \infty}\left(7 \log{\left(x \right)} \operatorname{atan}{\left(x \right)}\right) = \infty
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 (7*log(x))*atan(x), divided by x at x->+oo and x ->-oo
lim⁡x→−∞(7log⁡(x)atan⁡(x)x)=0\lim_{x \to -\infty}\left(\frac{7 \log{\left(x \right)} \operatorname{atan}{\left(x \right)}}{x}\right) = 0
Let's take the limit
so,
inclined coincides with the horizontal asymptote on the right
lim⁡x→∞(7log⁡(x)atan⁡(x)x)=0\lim_{x \to \infty}\left(\frac{7 \log{\left(x \right)} \operatorname{atan}{\left(x \right)}}{x}\right) = 0
Let's take the limit
so,
inclined coincides with the horizontal asymptote on the left
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:
7log⁡(x)atan⁡(x)=−7log⁡(−x)atan⁡(x)7 \log{\left(x \right)} \operatorname{atan}{\left(x \right)} = - 7 \log{\left(- x \right)} \operatorname{atan}{\left(x \right)}
- No
7log⁡(x)atan⁡(x)=7log⁡(−x)atan⁡(x)7 \log{\left(x \right)} \operatorname{atan}{\left(x \right)} = 7 \log{\left(- x \right)} \operatorname{atan}{\left(x \right)}
- No
so, the function
not is
neither even, nor odd
    © Mister Exam – Calculator