Mister Exam
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How to use it?
- Limit of the function:
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Limit of sin(z)
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Limit of cot(pi*x)*sin(x)/(2*sec(x))
- Limit of (x^4-a^4)/(x-a)
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Limit of cosh(1/x)
- Integral of d{x}:
- sin(z)
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Identical expressions
- sin(z)
- sinus of (z)
- sinz
Limit of the function sin(z)
The solution
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lim sin(z) z->oo
$$\lim_{z \to \infty} \sin{\left(z \right)}$$
Limit(sin(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
$$\lim_{z \to \infty} \sin{\left(z \right)} = \left\langle -1, 1\right\rangle$$
$$\lim_{z \to 0^-} \sin{\left(z \right)} = 0$$
More at z→0 from the left
$$\lim_{z \to 0^+} \sin{\left(z \right)} = 0$$
More at z→0 from the right
$$\lim_{z \to 1^-} \sin{\left(z \right)} = \sin{\left(1 \right)}$$
More at z→1 from the left
$$\lim_{z \to 1^+} \sin{\left(z \right)} = \sin{\left(1 \right)}$$
More at z→1 from the right
$$\lim_{z \to -\infty} \sin{\left(z \right)} = \left\langle -1, 1\right\rangle$$
More at z→-oo
$$\lim_{z \to 0^-} \sin{\left(z \right)} = 0$$
More at z→0 from the left
$$\lim_{z \to 0^+} \sin{\left(z \right)} = 0$$
More at z→0 from the right
$$\lim_{z \to 1^-} \sin{\left(z \right)} = \sin{\left(1 \right)}$$
More at z→1 from the left
$$\lim_{z \to 1^+} \sin{\left(z \right)} = \sin{\left(1 \right)}$$
More at z→1 from the right
$$\lim_{z \to -\infty} \sin{\left(z \right)} = \left\langle -1, 1\right\rangle$$
More at z→-oo
The graph