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

Limit of the function sin(x/3)

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The solution

You have entered [src] 
        /x\
 lim sin|-|
x->0+   \3/
$$\lim_{x \to 0^+} \sin{\left(\frac{x}{3} \right)}$$ 
Limit(sin(x/3), 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] 
        /x\
 lim sin|-|
x->0+   \3/
$$\lim_{x \to 0^+} \sin{\left(\frac{x}{3} \right)}$$ 
0
$$0$$ 
= -2.24227627745665e-34
        /x\
 lim sin|-|
x->0-   \3/
$$\lim_{x \to 0^-} \sin{\left(\frac{x}{3} \right)}$$ 
0
$$0$$ 
= 2.24227627745665e-34
= 2.24227627745665e-34
Rapid solution [src] 
0
$$0$$
Expand and simplify
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-} \sin{\left(\frac{x}{3} \right)} = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+} \sin{\left(\frac{x}{3} \right)} = 0$$
$$\lim_{x \to \infty} \sin{\left(\frac{x}{3} \right)} = \left\langle -1, 1\right\rangle$$
More at x→oo
$$\lim_{x \to 1^-} \sin{\left(\frac{x}{3} \right)} = \sin{\left(\frac{1}{3} \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \sin{\left(\frac{x}{3} \right)} = \sin{\left(\frac{1}{3} \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \sin{\left(\frac{x}{3} \right)} = \left\langle -1, 1\right\rangle$$
More at x→-oo
Numerical answer [src] 
-2.24227627745665e-34
-2.24227627745665e-34
The graph
Limit of the function sin(x/3)
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