Mister Exam

Limit of the function cos(z)

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The solution

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 lim cos(z)
z->0+      
$$\lim_{z \to 0^+} \cos{\left(z \right)}$$
Limit(cos(z), z, 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
One‐sided limits [src]
 lim cos(z)
z->0+      
$$\lim_{z \to 0^+} \cos{\left(z \right)}$$
1
$$1$$
= 1
 lim cos(z)
z->0-      
$$\lim_{z \to 0^-} \cos{\left(z \right)}$$
1
$$1$$
= 1
= 1
Other limits z→0, -oo, +oo, 1
$$\lim_{z \to 0^-} \cos{\left(z \right)} = 1$$
More at z→0 from the left
$$\lim_{z \to 0^+} \cos{\left(z \right)} = 1$$
$$\lim_{z \to \infty} \cos{\left(z \right)} = \left\langle -1, 1\right\rangle$$
More at z→oo
$$\lim_{z \to 1^-} \cos{\left(z \right)} = \cos{\left(1 \right)}$$
More at z→1 from the left
$$\lim_{z \to 1^+} \cos{\left(z \right)} = \cos{\left(1 \right)}$$
More at z→1 from the right
$$\lim_{z \to -\infty} \cos{\left(z \right)} = \left\langle -1, 1\right\rangle$$
More at z→-oo
Rapid solution [src]
1
$$1$$
Numerical answer [src]
1.0
1.0
The graph
Limit of the function cos(z)