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atan(5*x)
Limit of the function/ atan(5*x)

Limit of the function atan(5*x)

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The solution

You have entered [src] 
 lim atan(5*x)
x->0+
lim⁡x→0+atan⁡(5x)\lim_{x \to 0^+} \operatorname{atan}{\left(5 x \right)} 
Limit(atan(5*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
02468-8-6-4-2-10105-5
Plot the graph
Rapid solution [src] 
0
00
Expand and simplify
One‐sided limits [src] 
 lim atan(5*x)
x->0+
lim⁡x→0+atan⁡(5x)\lim_{x \to 0^+} \operatorname{atan}{\left(5 x \right)} 
0
00 
= 6.62006561323233e-30
 lim atan(5*x)
x->0-
lim⁡x→0−atan⁡(5x)\lim_{x \to 0^-} \operatorname{atan}{\left(5 x \right)} 
0
00 
= -6.62006561323233e-30
= -6.62006561323233e-30
Other limits x→0, -oo, +oo, 1
lim⁡x→0−atan⁡(5x)=0\lim_{x \to 0^-} \operatorname{atan}{\left(5 x \right)} = 0
More at x→0 from the left
lim⁡x→0+atan⁡(5x)=0\lim_{x \to 0^+} \operatorname{atan}{\left(5 x \right)} = 0
lim⁡x→∞atan⁡(5x)=π2\lim_{x \to \infty} \operatorname{atan}{\left(5 x \right)} = \frac{\pi}{2}
More at x→oo
lim⁡x→1−atan⁡(5x)=atan⁡(5)\lim_{x \to 1^-} \operatorname{atan}{\left(5 x \right)} = \operatorname{atan}{\left(5 \right)}
More at x→1 from the left
lim⁡x→1+atan⁡(5x)=atan⁡(5)\lim_{x \to 1^+} \operatorname{atan}{\left(5 x \right)} = \operatorname{atan}{\left(5 \right)}
More at x→1 from the right
lim⁡x→−∞atan⁡(5x)=−π2\lim_{x \to -\infty} \operatorname{atan}{\left(5 x \right)} = - \frac{\pi}{2}
More at x→-oo
Numerical answer [src] 
6.62006561323233e-30
6.62006561323233e-30
The graph
Limit of the function atan(5*x)
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