Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of sin(log(x))
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Limit of sin(x)/x
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Limit of sin(1/z)/(1-z)
- Limit of x/sqrt(x^2+y^2)
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Identical expressions
- sin(one /z)/(one -z)
- sinus of (1 divide by z) divide by (1 minus z)
- sinus of (one divide by z) divide by (one minus z)
- sin1/z/1-z
- sin(1 divide by z) divide by (1-z)
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Similar expressions
- sin(1/z)/(1+z)
Limit of the function sin(1/z)/(1-z)
The solution
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[src]
/ /1\\
|sin|-||
| \z/|
lim |------|
z->0+\1 - z /
$$\lim_{z \to 0^+}\left(\frac{\sin{\left(\frac{1}{z} \right)}}{1 - z}\right)$$
Limit(sin(1/z)/(1 - 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]
/ /1\\
|sin|-||
| \z/|
lim |------|
z->0+\1 - z /
$$\lim_{z \to 0^+}\left(\frac{\sin{\left(\frac{1}{z} \right)}}{1 - z}\right)$$
<-1, 1>
$$\left\langle -1, 1\right\rangle$$
= 1.32571003602926e-20
/ /1\\
|sin|-||
| \z/|
lim |------|
z->0-\1 - z /
$$\lim_{z \to 0^-}\left(\frac{\sin{\left(\frac{1}{z} \right)}}{1 - z}\right)$$
<-1, 1>
$$\left\langle -1, 1\right\rangle$$
= 7.20187738860025e-19
= 7.20187738860025e-19
Other limits z→0, -oo, +oo, 1
$$\lim_{z \to 0^-}\left(\frac{\sin{\left(\frac{1}{z} \right)}}{1 - z}\right) = \left\langle -1, 1\right\rangle$$
More at z→0 from the left
$$\lim_{z \to 0^+}\left(\frac{\sin{\left(\frac{1}{z} \right)}}{1 - z}\right) = \left\langle -1, 1\right\rangle$$
$$\lim_{z \to \infty}\left(\frac{\sin{\left(\frac{1}{z} \right)}}{1 - z}\right) = 0$$
More at z→oo
$$\lim_{z \to 1^-}\left(\frac{\sin{\left(\frac{1}{z} \right)}}{1 - z}\right) = \infty$$
More at z→1 from the left
$$\lim_{z \to 1^+}\left(\frac{\sin{\left(\frac{1}{z} \right)}}{1 - z}\right) = -\infty$$
More at z→1 from the right
$$\lim_{z \to -\infty}\left(\frac{\sin{\left(\frac{1}{z} \right)}}{1 - z}\right) = 0$$
More at z→-oo
More at z→0 from the left
$$\lim_{z \to 0^+}\left(\frac{\sin{\left(\frac{1}{z} \right)}}{1 - z}\right) = \left\langle -1, 1\right\rangle$$
$$\lim_{z \to \infty}\left(\frac{\sin{\left(\frac{1}{z} \right)}}{1 - z}\right) = 0$$
More at z→oo
$$\lim_{z \to 1^-}\left(\frac{\sin{\left(\frac{1}{z} \right)}}{1 - z}\right) = \infty$$
More at z→1 from the left
$$\lim_{z \to 1^+}\left(\frac{\sin{\left(\frac{1}{z} \right)}}{1 - z}\right) = -\infty$$
More at z→1 from the right
$$\lim_{z \to -\infty}\left(\frac{\sin{\left(\frac{1}{z} \right)}}{1 - z}\right) = 0$$
More at z→-oo
The graph