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tan(3*x)^2
Limit of the function/ tan(3*x)^2

Limit of the function tan(3*x)^2

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        2     
 lim tan (3*x)
x->0+
lim⁡x→0+tan⁡2(3x)\lim_{x \to 0^+} \tan^{2}{\left(3 x \right)} 
Limit(tan(3*x)^2, 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
02468-8-6-4-2-1010-5000050000
Plot the graph
Other limits x→0, -oo, +oo, 1
lim⁡x→0−tan⁡2(3x)=0\lim_{x \to 0^-} \tan^{2}{\left(3 x \right)} = 0
More at x→0 from the left
lim⁡x→0+tan⁡2(3x)=0\lim_{x \to 0^+} \tan^{2}{\left(3 x \right)} = 0
lim⁡x→∞tan⁡2(3x)=⟨0,∞⟩\lim_{x \to \infty} \tan^{2}{\left(3 x \right)} = \left\langle 0, \infty\right\rangle
More at x→oo
lim⁡x→1−tan⁡2(3x)=tan⁡2(3)\lim_{x \to 1^-} \tan^{2}{\left(3 x \right)} = \tan^{2}{\left(3 \right)}
More at x→1 from the left
lim⁡x→1+tan⁡2(3x)=tan⁡2(3)\lim_{x \to 1^+} \tan^{2}{\left(3 x \right)} = \tan^{2}{\left(3 \right)}
More at x→1 from the right
lim⁡x→−∞tan⁡2(3x)=⟨0,∞⟩\lim_{x \to -\infty} \tan^{2}{\left(3 x \right)} = \left\langle 0, \infty\right\rangle
More at x→-oo
Rapid solution [src] 
0
00
Expand and simplify
One‐sided limits [src] 
        2     
 lim tan (3*x)
x->0+
lim⁡x→0+tan⁡2(3x)\lim_{x \to 0^+} \tan^{2}{\left(3 x \right)} 
0
00 
= -1.52383419835679e-32
        2     
 lim tan (3*x)
x->0-
lim⁡x→0−tan⁡2(3x)\lim_{x \to 0^-} \tan^{2}{\left(3 x \right)} 
0
00 
= -1.52383419835679e-32
= -1.52383419835679e-32
Numerical answer [src] 
-1.52383419835679e-32
-1.52383419835679e-32
The graph
Limit of the function tan(3*x)^2
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