Mister Exam
Other calculators
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-
How to use it?
- Graphing y =:
- (x+2)^2/(x+1)
- x^6+x^3-2
- (x+2)/(x-3)
- x^2-5x-3
- Derivative of:
-
4*sin(x)-5*cot(x)
-
Identical expressions
- four *sin(x)- five *cot(x)
- 4 multiply by sinus of (x) minus 5 multiply by cotangent of (x)
- four multiply by sinus of (x) minus five multiply by cotangent of (x)
- 4sin(x)-5cot(x)
- 4sinx-5cotx
-
Similar expressions
- 4*sin(x)+5*cot(x)
- 4*sinx-5*cot(x)
Graphing y = 4*sin(x)-5*cot(x)
The solution
You have entered
[src]
f(x) = 4*sin(x) - 5*cot(x)
$$f{\left(x \right)} = 4 \sin{\left(x \right)} - 5 \cot{\left(x \right)}$$
f = 4*sin(x) - 5*cot(x)
The graph of the function
Horizontal asymptotes
Let’s find horizontal asymptotes with help of the limits of this function at x->+oo and x->-oo
Let's take the limit
so,
equation of the horizontal asymptote on the left:
$$y = \lim_{x \to -\infty}\left(4 \sin{\left(x \right)} - 5 \cot{\left(x \right)}\right)$$
Let's take the limit
so,
equation of the horizontal asymptote on the right:
$$y = \lim_{x \to \infty}\left(4 \sin{\left(x \right)} - 5 \cot{\left(x \right)}\right)$$
True
Let's take the limit
so,
equation of the horizontal asymptote on the left:
$$y = \lim_{x \to -\infty}\left(4 \sin{\left(x \right)} - 5 \cot{\left(x \right)}\right)$$
True
Let's take the limit
so,
equation of the horizontal asymptote on the right:
$$y = \lim_{x \to \infty}\left(4 \sin{\left(x \right)} - 5 \cot{\left(x \right)}\right)$$
Inclined asymptotes
Inclined asymptote can be found by calculating the limit of 4*sin(x) - 5*cot(x), divided by x at x->+oo and x ->-oo
Let's take the limit
so,
inclined asymptote equation on the left:
$$y = x \lim_{x \to -\infty}\left(\frac{4 \sin{\left(x \right)} - 5 \cot{\left(x \right)}}{x}\right)$$
Let's take the limit
so,
inclined asymptote equation on the right:
$$y = x \lim_{x \to \infty}\left(\frac{4 \sin{\left(x \right)} - 5 \cot{\left(x \right)}}{x}\right)$$
True
Let's take the limit
so,
inclined asymptote equation on the left:
$$y = x \lim_{x \to -\infty}\left(\frac{4 \sin{\left(x \right)} - 5 \cot{\left(x \right)}}{x}\right)$$
True
Let's take the limit
so,
inclined asymptote equation on the right:
$$y = x \lim_{x \to \infty}\left(\frac{4 \sin{\left(x \right)} - 5 \cot{\left(x \right)}}{x}\right)$$
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:
$$4 \sin{\left(x \right)} - 5 \cot{\left(x \right)} = - 4 \sin{\left(x \right)} + 5 \cot{\left(x \right)}$$
- No
$$4 \sin{\left(x \right)} - 5 \cot{\left(x \right)} = 4 \sin{\left(x \right)} - 5 \cot{\left(x \right)}$$
- No
so, the function
not is
neither even, nor odd
So, check:
$$4 \sin{\left(x \right)} - 5 \cot{\left(x \right)} = - 4 \sin{\left(x \right)} + 5 \cot{\left(x \right)}$$
- No
$$4 \sin{\left(x \right)} - 5 \cot{\left(x \right)} = 4 \sin{\left(x \right)} - 5 \cot{\left(x \right)}$$
- No
so, the function
not is
neither even, nor odd