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

Limit of the function atan(1/x)

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         /  1\
 lim atan|1*-|
x->0+    \  x/
$$\lim_{x \to 0^+} \operatorname{atan}{\left(1 \cdot \frac{1}{x} \right)}$$ 
Limit(atan(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
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-} \operatorname{atan}{\left(1 \cdot \frac{1}{x} \right)} = \frac{\pi}{2}$$
More at x→0 from the left
$$\lim_{x \to 0^+} \operatorname{atan}{\left(1 \cdot \frac{1}{x} \right)} = \frac{\pi}{2}$$
$$\lim_{x \to \infty} \operatorname{atan}{\left(1 \cdot \frac{1}{x} \right)} = 0$$
More at x→oo
$$\lim_{x \to 1^-} \operatorname{atan}{\left(1 \cdot \frac{1}{x} \right)} = \frac{\pi}{4}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \operatorname{atan}{\left(1 \cdot \frac{1}{x} \right)} = \frac{\pi}{4}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \operatorname{atan}{\left(1 \cdot \frac{1}{x} \right)} = 0$$
More at x→-oo
One‐sided limits [src] 
         /  1\
 lim atan|1*-|
x->0+    \  x/
$$\lim_{x \to 0^+} \operatorname{atan}{\left(1 \cdot \frac{1}{x} \right)}$$ 
pi
--
2
$$\frac{\pi}{2}$$ 
= 1.5707963267949
         /  1\
 lim atan|1*-|
x->0-    \  x/
$$\lim_{x \to 0^-} \operatorname{atan}{\left(1 \cdot \frac{1}{x} \right)}$$ 
-pi 
----
 2
$$- \frac{\pi}{2}$$ 
= -1.5707963267949
= -1.5707963267949
Rapid solution [src] 
pi
--
2
$$\frac{\pi}{2}$$
Expand and simplify
Numerical answer [src] 
1.5707963267949
1.5707963267949
The graph
Limit of the function atan(1/x)
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