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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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You have entered [src] 
 lim  cos(3*x)
x->pi+
lim⁡x→π+cos⁡(3x)\lim_{x \to \pi^+} \cos{\left(3 x \right)} 
Limit(cos(3*x), x, pi)
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
0123456-6-5-4-3-2-12-2
Plot the graph
Rapid solution [src] 
-1
−1-1
Expand and simplify
One‐sided limits [src] 
 lim  cos(3*x)
x->pi+
lim⁡x→π+cos⁡(3x)\lim_{x \to \pi^+} \cos{\left(3 x \right)} 
-1
−1-1 
= -1.0
 lim  cos(3*x)
x->pi-
lim⁡x→π−cos⁡(3x)\lim_{x \to \pi^-} \cos{\left(3 x \right)} 
-1
−1-1 
= -1.0
= -1.0
Other limits x→0, -oo, +oo, 1
lim⁡x→π−cos⁡(3x)=−1\lim_{x \to \pi^-} \cos{\left(3 x \right)} = -1
More at x→pi from the left
lim⁡x→π+cos⁡(3x)=−1\lim_{x \to \pi^+} \cos{\left(3 x \right)} = -1
lim⁡x→∞cos⁡(3x)=⟨−1,1⟩\lim_{x \to \infty} \cos{\left(3 x \right)} = \left\langle -1, 1\right\rangle
More at x→oo
lim⁡x→0−cos⁡(3x)=1\lim_{x \to 0^-} \cos{\left(3 x \right)} = 1
More at x→0 from the left
lim⁡x→0+cos⁡(3x)=1\lim_{x \to 0^+} \cos{\left(3 x \right)} = 1
More at x→0 from the right
lim⁡x→1−cos⁡(3x)=cos⁡(3)\lim_{x \to 1^-} \cos{\left(3 x \right)} = \cos{\left(3 \right)}
More at x→1 from the left
lim⁡x→1+cos⁡(3x)=cos⁡(3)\lim_{x \to 1^+} \cos{\left(3 x \right)} = \cos{\left(3 \right)}
More at x→1 from the right
lim⁡x→−∞cos⁡(3x)=⟨−1,1⟩\lim_{x \to -\infty} \cos{\left(3 x \right)} = \left\langle -1, 1\right\rangle
More at x→-oo
Numerical answer [src] 
-1.0
-1.0
The graph
Limit of the function cos(3*x)
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