Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of x^(4/x)
-
Limit of (-6+x^2-x)/(-4+x^2)
-
Limit of (-6+x^2-x)/(-21+x+2*x^2)
-
Limit of e^(3-x)*(-2+x)
-
Identical expressions
- (cos(x)+sin(x))/x
- ( co sinus of e of (x) plus sinus of (x)) divide by x
- cosx+sinx/x
- (cos(x)+sin(x)) divide by x
-
Similar expressions
- (cos(x)-sin(x))/x
- (-cos(x)+sin(x))/x^3
- (-x*cos(x)+sin(x))/(x^2*tan(x))
- (cosx+sinx)/x
Limit of the function (cos(x)+sin(x))/x
The solution
You have entered
[src]
/cos(x) + sin(x)\ lim |---------------| x->oo\ x /
$$\lim_{x \to \infty}\left(\frac{\sin{\left(x \right)} + \cos{\left(x \right)}}{x}\right)$$
Limit((cos(x) + sin(x))/x, x, oo, dir='-')
Lopital's rule
There is no sense to apply Lopital's rule to this function since there is no indeterminateness of 0/0 or oo/oo type
The graph
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \infty}\left(\frac{\sin{\left(x \right)} + \cos{\left(x \right)}}{x}\right) = 0$$
$$\lim_{x \to 0^-}\left(\frac{\sin{\left(x \right)} + \cos{\left(x \right)}}{x}\right) = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\sin{\left(x \right)} + \cos{\left(x \right)}}{x}\right) = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{\sin{\left(x \right)} + \cos{\left(x \right)}}{x}\right) = \cos{\left(1 \right)} + \sin{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\sin{\left(x \right)} + \cos{\left(x \right)}}{x}\right) = \cos{\left(1 \right)} + \sin{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\sin{\left(x \right)} + \cos{\left(x \right)}}{x}\right) = 0$$
More at x→-oo
$$\lim_{x \to 0^-}\left(\frac{\sin{\left(x \right)} + \cos{\left(x \right)}}{x}\right) = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\sin{\left(x \right)} + \cos{\left(x \right)}}{x}\right) = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{\sin{\left(x \right)} + \cos{\left(x \right)}}{x}\right) = \cos{\left(1 \right)} + \sin{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\sin{\left(x \right)} + \cos{\left(x \right)}}{x}\right) = \cos{\left(1 \right)} + \sin{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\sin{\left(x \right)} + \cos{\left(x \right)}}{x}\right) = 0$$
More at x→-oo
The graph