Mister Exam
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How to use it?
- Limit of the function:
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Limit of (1+n)^3/n^3
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Limit of sin(1/z)
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Limit of 8/x
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Limit of z^4
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Identical expressions
- sin(one /z)
- sinus of (1 divide by z)
- sinus of (one divide by z)
- sin1/z
- sin(1 divide by z)
Limit of the function sin(1/z)
The solution
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/ 1\ lim sin|1*-| z->oo \ z/
$$\lim_{z \to \infty} \sin{\left(1 \cdot \frac{1}{z} \right)}$$
Limit(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
Other limits z→0, -oo, +oo, 1
$$\lim_{z \to \infty} \sin{\left(1 \cdot \frac{1}{z} \right)} = 0$$
$$\lim_{z \to 0^-} \sin{\left(1 \cdot \frac{1}{z} \right)} = \left\langle -1, 1\right\rangle$$
More at z→0 from the left
$$\lim_{z \to 0^+} \sin{\left(1 \cdot \frac{1}{z} \right)} = \left\langle -1, 1\right\rangle$$
More at z→0 from the right
$$\lim_{z \to 1^-} \sin{\left(1 \cdot \frac{1}{z} \right)} = \sin{\left(1 \right)}$$
More at z→1 from the left
$$\lim_{z \to 1^+} \sin{\left(1 \cdot \frac{1}{z} \right)} = \sin{\left(1 \right)}$$
More at z→1 from the right
$$\lim_{z \to -\infty} \sin{\left(1 \cdot \frac{1}{z} \right)} = 0$$
More at z→-oo
$$\lim_{z \to 0^-} \sin{\left(1 \cdot \frac{1}{z} \right)} = \left\langle -1, 1\right\rangle$$
More at z→0 from the left
$$\lim_{z \to 0^+} \sin{\left(1 \cdot \frac{1}{z} \right)} = \left\langle -1, 1\right\rangle$$
More at z→0 from the right
$$\lim_{z \to 1^-} \sin{\left(1 \cdot \frac{1}{z} \right)} = \sin{\left(1 \right)}$$
More at z→1 from the left
$$\lim_{z \to 1^+} \sin{\left(1 \cdot \frac{1}{z} \right)} = \sin{\left(1 \right)}$$
More at z→1 from the right
$$\lim_{z \to -\infty} \sin{\left(1 \cdot \frac{1}{z} \right)} = 0$$
More at z→-oo
The graph