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

Limit of the function sin(1/x)

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You have entered [src] 
        /1\
 lim sin|-|
x->0+   \x/
$$\lim_{x \to 0^+} \sin{\left(\frac{1}{x} \right)}$$ 
Limit(sin(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
One‐sided limits [src] 
        /1\
 lim sin|-|
x->0+   \x/
$$\lim_{x \to 0^+} \sin{\left(\frac{1}{x} \right)}$$ 
<-1, 1>
$$\left\langle -1, 1\right\rangle$$ 
= 5.27928954763288e-76
        /1\
 lim sin|-|
x->0-   \x/
$$\lim_{x \to 0^-} \sin{\left(\frac{1}{x} \right)}$$ 
<-1, 1>
$$\left\langle -1, 1\right\rangle$$ 
= -5.27928954763288e-76
= -5.27928954763288e-76
Rapid solution [src] 
<-1, 1>
$$\left\langle -1, 1\right\rangle$$
Expand and simplify
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-} \sin{\left(\frac{1}{x} \right)} = \left\langle -1, 1\right\rangle$$
More at x→0 from the left
$$\lim_{x \to 0^+} \sin{\left(\frac{1}{x} \right)} = \left\langle -1, 1\right\rangle$$
$$\lim_{x \to \infty} \sin{\left(\frac{1}{x} \right)} = 0$$
More at x→oo
$$\lim_{x \to 1^-} \sin{\left(\frac{1}{x} \right)} = \sin{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \sin{\left(\frac{1}{x} \right)} = \sin{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \sin{\left(\frac{1}{x} \right)} = 0$$
More at x→-oo
Numerical answer [src] 
5.27928954763288e-76
5.27928954763288e-76
The graph
Limit of the function sin(1/x)
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