Mister Exam
Other calculators
- Graph of implicit function
- Derivative Step by Step
- Integral Step by Step
- Graph of parametric function
- Graph in Polar Coordinates
- Surface defined parametrically
- Surface defined by equation
- Curve in 3D space defined parametrically
- Area between lines
- The intersection points of functions
-
How to use it?
- Graphing y =:
- 3y*log(y)-(1/36)*exp(-(36y-(36/e))^4)
- sqrt(6x-1)
-
log0.2x
-
sin(ln(x))
-
Identical expressions
- 3y*log(y)-(one / thirty-six)*exp(-(thirty-six y-(36/e))^ four)
- 3y multiply by logarithm of (y) minus (1 divide by 36) multiply by exponent of ( minus (36y minus (36 divide by e)) to the power of 4)
- 3y multiply by logarithm of (y) minus (one divide by thirty minus six) multiply by exponent of ( minus (thirty minus six y minus (36 divide by e)) to the power of four)
- 3y*log(y)-(1/36)*exp(-(36y-(36/e))4)
- 3y*logy-1/36*exp-36y-36/e4
- 3y*log(y)-(1/36)*exp(-(36y-(36/e))⁴)
- 3ylog(y)-(1/36)exp(-(36y-(36/e))^4)
- 3ylog(y)-(1/36)exp(-(36y-(36/e))4)
- 3ylogy-1/36exp-36y-36/e4
- 3ylogy-1/36exp-36y-36/e^4
- 3y*log(y)-(1 divide by 36)*exp(-(36y-(36 divide by e))^4)
-
Similar expressions
- 3y*log(y)-(1/36)*exp(-(36y+(36/e))^4)
- 3y*log(y)+(1/36)*exp(-(36y-(36/e))^4)
- 3y*log(y)-(1/36)*exp((36y-(36/e))^4)
Graphing y = 3y*log(y)-(1/36)*exp(-(36y-(36/e))^4)
The solution
You have entered
[src]
4
/ 36\
-|36*y - --|
\ E /
e
f(y) = 3*y*log(y) - --------------
36
$$f{\left(y \right)} = 3 y \log{\left(y \right)} - \frac{e^{- \left(36 y - \frac{36}{e}\right)^{4}}}{36}$$
f = (3*y)*log(y) - exp(-(36*y - 36*exp(-1))^4)/36
The graph of the function
Horizontal asymptotes
Let’s find horizontal asymptotes with help of the limits of this function at y->+oo and y->-oo
$$\lim_{y \to -\infty}\left(3 y \log{\left(y \right)} - \frac{e^{- \left(36 y - \frac{36}{e}\right)^{4}}}{36}\right) = -\infty$$
Let's take the limit
so,
horizontal asymptote on the left doesn’t exist
$$\lim_{y \to \infty}\left(3 y \log{\left(y \right)} - \frac{e^{- \left(36 y - \frac{36}{e}\right)^{4}}}{36}\right) = \infty$$
Let's take the limit
so,
horizontal asymptote on the right doesn’t exist
$$\lim_{y \to -\infty}\left(3 y \log{\left(y \right)} - \frac{e^{- \left(36 y - \frac{36}{e}\right)^{4}}}{36}\right) = -\infty$$
Let's take the limit
so,
horizontal asymptote on the left doesn’t exist
$$\lim_{y \to \infty}\left(3 y \log{\left(y \right)} - \frac{e^{- \left(36 y - \frac{36}{e}\right)^{4}}}{36}\right) = \infty$$
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 (3*y)*log(y) - exp(-(36*y - 36*exp(-1))^4)/36, divided by y at y->+oo and y ->-oo
$$\lim_{y \to -\infty}\left(\frac{3 y \log{\left(y \right)} - \frac{e^{- \left(36 y - \frac{36}{e}\right)^{4}}}{36}}{y}\right) = \infty$$
Let's take the limit
so,
inclined asymptote on the left doesn’t exist
$$\lim_{y \to \infty}\left(\frac{3 y \log{\left(y \right)} - \frac{e^{- \left(36 y - \frac{36}{e}\right)^{4}}}{36}}{y}\right) = \infty$$
Let's take the limit
so,
inclined asymptote on the right doesn’t exist
$$\lim_{y \to -\infty}\left(\frac{3 y \log{\left(y \right)} - \frac{e^{- \left(36 y - \frac{36}{e}\right)^{4}}}{36}}{y}\right) = \infty$$
Let's take the limit
so,
inclined asymptote on the left doesn’t exist
$$\lim_{y \to \infty}\left(\frac{3 y \log{\left(y \right)} - \frac{e^{- \left(36 y - \frac{36}{e}\right)^{4}}}{36}}{y}\right) = \infty$$
Let's take the limit
so,
inclined asymptote on the right doesn’t exist
Even and odd functions
Let's check, whether the function even or odd by using relations f = f(-y) и f = -f(-y).
So, check:
$$3 y \log{\left(y \right)} - \frac{e^{- \left(36 y - \frac{36}{e}\right)^{4}}}{36} = - 3 y \log{\left(- y \right)} - \frac{e^{- \left(- 36 y - \frac{36}{e}\right)^{4}}}{36}$$
- No
$$3 y \log{\left(y \right)} - \frac{e^{- \left(36 y - \frac{36}{e}\right)^{4}}}{36} = 3 y \log{\left(- y \right)} + \frac{e^{- \left(- 36 y - \frac{36}{e}\right)^{4}}}{36}$$
- No
so, the function
not is
neither even, nor odd
So, check:
$$3 y \log{\left(y \right)} - \frac{e^{- \left(36 y - \frac{36}{e}\right)^{4}}}{36} = - 3 y \log{\left(- y \right)} - \frac{e^{- \left(- 36 y - \frac{36}{e}\right)^{4}}}{36}$$
- No
$$3 y \log{\left(y \right)} - \frac{e^{- \left(36 y - \frac{36}{e}\right)^{4}}}{36} = 3 y \log{\left(- y \right)} + \frac{e^{- \left(- 36 y - \frac{36}{e}\right)^{4}}}{36}$$
- No
so, the function
not is
neither even, nor odd