Mister Exam

Other calculators:

cos(1/x)
Limit of the function/ cos(1/x)

Limit of the function cos(1/x)

at →
v

For end points:

The graph:

from to

Piecewise:

The solution

You have entered [src] 
        /  1\
 lim cos|1*-|
x->0+   \  x/
$$\lim_{x \to 0^+} \cos{\left(1 \cdot \frac{1}{x} \right)}$$ 
Limit(cos(1/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] 
<-1, 1>
$$\left\langle -1, 1\right\rangle$$
Expand and simplify
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-} \cos{\left(1 \cdot \frac{1}{x} \right)} = \left\langle -1, 1\right\rangle$$
More at x→0 from the left
$$\lim_{x \to 0^+} \cos{\left(1 \cdot \frac{1}{x} \right)} = \left\langle -1, 1\right\rangle$$
$$\lim_{x \to \infty} \cos{\left(1 \cdot \frac{1}{x} \right)} = 1$$
More at x→oo
$$\lim_{x \to 1^-} \cos{\left(1 \cdot \frac{1}{x} \right)} = \cos{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \cos{\left(1 \cdot \frac{1}{x} \right)} = \cos{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \cos{\left(1 \cdot \frac{1}{x} \right)} = 1$$
More at x→-oo
One‐sided limits [src] 
        /  1\
 lim cos|1*-|
x->0+   \  x/
$$\lim_{x \to 0^+} \cos{\left(1 \cdot \frac{1}{x} \right)}$$ 
<-1, 1>
$$\left\langle -1, 1\right\rangle$$ 
= -1.83036708622755e-76
        /  1\
 lim cos|1*-|
x->0-   \  x/
$$\lim_{x \to 0^-} \cos{\left(1 \cdot \frac{1}{x} \right)}$$ 
<-1, 1>
$$\left\langle -1, 1\right\rangle$$ 
= -1.83036708622755e-76
= -1.83036708622755e-76
Numerical answer [src] 
-1.83036708622755e-76
-1.83036708622755e-76
The graph
Limit of the function cos(1/x)
    © Mister Exam – Calculator