Mister Exam

Other calculators:

cos(x)/x
Limit of the function/ cos(x)/x

Limit of the function cos(x)/x

at →
v

For end points:

The graph:

from to

Piecewise:

The solution

You have entered [src] 
     /cos(x)\
 lim |------|
x->0+\  x   /
$$\lim_{x \to 0^+}\left(\frac{\cos{\left(x \right)}}{x}\right)$$ 
Limit(cos(x)/x, x, 0)
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
Plot the graph
Rapid solution [src] 
oo
$$\infty$$
Expand and simplify
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-}\left(\frac{\cos{\left(x \right)}}{x}\right) = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\cos{\left(x \right)}}{x}\right) = \infty$$
$$\lim_{x \to \infty}\left(\frac{\cos{\left(x \right)}}{x}\right) = 0$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{\cos{\left(x \right)}}{x}\right) = \cos{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\cos{\left(x \right)}}{x}\right) = \cos{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\cos{\left(x \right)}}{x}\right) = 0$$
More at x→-oo
One‐sided limits [src] 
     /cos(x)\
 lim |------|
x->0+\  x   /
$$\lim_{x \to 0^+}\left(\frac{\cos{\left(x \right)}}{x}\right)$$ 
oo
$$\infty$$ 
= 150.996688753824
     /cos(x)\
 lim |------|
x->0-\  x   /
$$\lim_{x \to 0^-}\left(\frac{\cos{\left(x \right)}}{x}\right)$$ 
-oo
$$-\infty$$ 
= -150.996688753824
= -150.996688753824
Numerical answer [src] 
150.996688753824
150.996688753824
The graph
Limit of the function cos(x)/x
    © Mister Exam – Calculator