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cos(3/x)
Limit of the function/ cos(3/x)

Limit of the function cos(3/x)

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        /3\
 lim cos|-|
x->0+   \x/
$$\lim_{x \to 0^+} \cos{\left(\frac{3}{x} \right)}$$ 
Limit(cos(3/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
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Rapid solution [src] 
<-1, 1>
$$\left\langle -1, 1\right\rangle$$
Expand and simplify
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-} \cos{\left(\frac{3}{x} \right)} = \left\langle -1, 1\right\rangle$$
More at x→0 from the left
$$\lim_{x \to 0^+} \cos{\left(\frac{3}{x} \right)} = \left\langle -1, 1\right\rangle$$
$$\lim_{x \to \infty} \cos{\left(\frac{3}{x} \right)} = 1$$
More at x→oo
$$\lim_{x \to 1^-} \cos{\left(\frac{3}{x} \right)} = \cos{\left(3 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \cos{\left(\frac{3}{x} \right)} = \cos{\left(3 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \cos{\left(\frac{3}{x} \right)} = 1$$
More at x→-oo
One‐sided limits [src] 
        /3\
 lim cos|-|
x->0+   \x/
$$\lim_{x \to 0^+} \cos{\left(\frac{3}{x} \right)}$$ 
<-1, 1>
$$\left\langle -1, 1\right\rangle$$ 
= -2.69564916612587e-77
        /3\
 lim cos|-|
x->0-   \x/
$$\lim_{x \to 0^-} \cos{\left(\frac{3}{x} \right)}$$ 
<-1, 1>
$$\left\langle -1, 1\right\rangle$$ 
= -2.69564916612587e-77
= -2.69564916612587e-77
Numerical answer [src] 
-2.69564916612587e-77
-2.69564916612587e-77
The graph
Limit of the function cos(3/x)
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