Mister Exam

Other calculators:

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

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

at →
v

For end points:

The graph:

from to

Piecewise:

The solution

You have entered [src] 
     /     /  1\\
 lim |z*sin|1*-||
z->oo\     \  z//
lim⁡z→∞(zsin⁡(1⋅1z))\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
The graph
02468-8-6-4-2-10102-1
Plot the graph
Rapid solution [src] 
1
11
Expand and simplify
Other limits z→0, -oo, +oo, 1
lim⁡z→∞(zsin⁡(1⋅1z))=1\lim_{z \to \infty}\left(z \sin{\left(1 \cdot \frac{1}{z} \right)}\right) = 1
lim⁡z→0−(zsin⁡(1⋅1z))=0\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→0+(zsin⁡(1⋅1z))=0\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→1−(zsin⁡(1⋅1z))=sin⁡(1)\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→1+(zsin⁡(1⋅1z))=sin⁡(1)\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→−∞(zsin⁡(1⋅1z))=1\lim_{z \to -\infty}\left(z \sin{\left(1 \cdot \frac{1}{z} \right)}\right) = 1
More at z→-oo
The graph
Limit of the function z*sin(1/z)
    © Mister Exam – Calculator