Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of ((-1+n)/n)^n
-
Limit of (log(x)+sin(x))/(x^2+2*log(x))
-
Limit of -3+3*x+55*x^2/6
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Limit of (9+2*n)/(5+2*n)
- Graphing y =:
- z^3*sin(3/z)
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Identical expressions
- z^ three *sin(three /z)
- z cubed multiply by sinus of (3 divide by z)
- z to the power of three multiply by sinus of (three divide by z)
- z3*sin(3/z)
- z3*sin3/z
- z³*sin(3/z)
- z to the power of 3*sin(3/z)
- z^3sin(3/z)
- z3sin(3/z)
- z3sin3/z
- z^3sin3/z
- z^3*sin(3 divide by z)
Limit of the function z^3*sin(3/z)
The solution
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[src]
/ 3 /3\\ lim |z *sin|-|| z->0+\ \z//
$$\lim_{z \to 0^+}\left(z^{3} \sin{\left(\frac{3}{z} \right)}\right)$$
Limit(z^3*sin(3/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]
/ 3 /3\\ lim |z *sin|-|| z->0+\ \z//
$$\lim_{z \to 0^+}\left(z^{3} \sin{\left(\frac{3}{z} \right)}\right)$$
0
$$0$$
= -2.75496046549099e-23
/ 3 /3\\ lim |z *sin|-|| z->0-\ \z//
$$\lim_{z \to 0^-}\left(z^{3} \sin{\left(\frac{3}{z} \right)}\right)$$
0
$$0$$
= -2.75496046549099e-23
= -2.75496046549099e-23
Other limits z→0, -oo, +oo, 1
$$\lim_{z \to 0^-}\left(z^{3} \sin{\left(\frac{3}{z} \right)}\right) = 0$$
More at z→0 from the left
$$\lim_{z \to 0^+}\left(z^{3} \sin{\left(\frac{3}{z} \right)}\right) = 0$$
$$\lim_{z \to \infty}\left(z^{3} \sin{\left(\frac{3}{z} \right)}\right) = \infty$$
More at z→oo
$$\lim_{z \to 1^-}\left(z^{3} \sin{\left(\frac{3}{z} \right)}\right) = \sin{\left(3 \right)}$$
More at z→1 from the left
$$\lim_{z \to 1^+}\left(z^{3} \sin{\left(\frac{3}{z} \right)}\right) = \sin{\left(3 \right)}$$
More at z→1 from the right
$$\lim_{z \to -\infty}\left(z^{3} \sin{\left(\frac{3}{z} \right)}\right) = \infty$$
More at z→-oo
More at z→0 from the left
$$\lim_{z \to 0^+}\left(z^{3} \sin{\left(\frac{3}{z} \right)}\right) = 0$$
$$\lim_{z \to \infty}\left(z^{3} \sin{\left(\frac{3}{z} \right)}\right) = \infty$$
More at z→oo
$$\lim_{z \to 1^-}\left(z^{3} \sin{\left(\frac{3}{z} \right)}\right) = \sin{\left(3 \right)}$$
More at z→1 from the left
$$\lim_{z \to 1^+}\left(z^{3} \sin{\left(\frac{3}{z} \right)}\right) = \sin{\left(3 \right)}$$
More at z→1 from the right
$$\lim_{z \to -\infty}\left(z^{3} \sin{\left(\frac{3}{z} \right)}\right) = \infty$$
More at z→-oo
The graph