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cos(x)^4
Limit of the function/ cos(x)^4

Limit of the function cos(x)^4

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        4   
 lim cos (x)
x->oo
lim⁡x→∞cos⁡4(x)\lim_{x \to \infty} \cos^{4}{\left(x \right)} 
Limit(cos(x)^4, x, oo, dir='-')
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
02468-8-6-4-2-101002
Plot the graph
Rapid solution [src] 
<0, 1>
⟨0,1⟩\left\langle 0, 1\right\rangle
Expand and simplify
Other limits x→0, -oo, +oo, 1
lim⁡x→∞cos⁡4(x)=⟨0,1⟩\lim_{x \to \infty} \cos^{4}{\left(x \right)} = \left\langle 0, 1\right\rangle
lim⁡x→0−cos⁡4(x)=1\lim_{x \to 0^-} \cos^{4}{\left(x \right)} = 1
More at x→0 from the left
lim⁡x→0+cos⁡4(x)=1\lim_{x \to 0^+} \cos^{4}{\left(x \right)} = 1
More at x→0 from the right
lim⁡x→1−cos⁡4(x)=cos⁡4(1)\lim_{x \to 1^-} \cos^{4}{\left(x \right)} = \cos^{4}{\left(1 \right)}
More at x→1 from the left
lim⁡x→1+cos⁡4(x)=cos⁡4(1)\lim_{x \to 1^+} \cos^{4}{\left(x \right)} = \cos^{4}{\left(1 \right)}
More at x→1 from the right
lim⁡x→−∞cos⁡4(x)=⟨0,1⟩\lim_{x \to -\infty} \cos^{4}{\left(x \right)} = \left\langle 0, 1\right\rangle
More at x→-oo
The graph
Limit of the function cos(x)^4
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