Mister Exam

# Limit of the function z*sin(1/z)

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### The solution

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lim |z*sin|1*-||
z->oo\     \  z//
$$\lim_{z \to \infty}\left(z \sin{\left(1 \cdot \frac{1}{z} \right)}\right)$$
Limit(z*sin(1/z), z, 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
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Rapid solution [src]
1
$$1$$
Other limits z→0, -oo, +oo, 1
$$\lim_{z \to \infty}\left(z \sin{\left(1 \cdot \frac{1}{z} \right)}\right) = 1$$
$$\lim_{z \to 0^-}\left(z \sin{\left(1 \cdot \frac{1}{z} \right)}\right) = 0$$
More at z→0 from the left
$$\lim_{z \to 0^+}\left(z \sin{\left(1 \cdot \frac{1}{z} \right)}\right) = 0$$
More at z→0 from the right
$$\lim_{z \to 1^-}\left(z \sin{\left(1 \cdot \frac{1}{z} \right)}\right) = \sin{\left(1 \right)}$$
More at z→1 from the left
$$\lim_{z \to 1^+}\left(z \sin{\left(1 \cdot \frac{1}{z} \right)}\right) = \sin{\left(1 \right)}$$
More at z→1 from the right
$$\lim_{z \to -\infty}\left(z \sin{\left(1 \cdot \frac{1}{z} \right)}\right) = 1$$
More at z→-oo
The graph