Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-21+x^2+4*x)/(7+x)
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Limit of (-3+x^2+2*x)/(1-3*x+2*x^2)
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Limit of -1+sqrt(5)-x-2/(sqrt(2)-x)
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Limit of (-2+sqrt(3+cos(x)))/x^2
- Derivative of:
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z*sin(z)
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Identical expressions
- z*sin(z)
- z multiply by sinus of (z)
- zsin(z)
- zsinz
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Similar expressions
- z/((1-cos(z))*sin(z))
- z^2/(cos(z)*sin(z)^3)
Limit of the function z*sin(z)
The solution
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[src]
lim (z*sin(z)) z->-1+
$$\lim_{z \to -1^+}\left(z \sin{\left(z \right)}\right)$$
Limit(z*sin(z), z, -1)
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
$$\lim_{z \to -1^-}\left(z \sin{\left(z \right)}\right) = \sin{\left(1 \right)}$$
More at z→-1 from the left
$$\lim_{z \to -1^+}\left(z \sin{\left(z \right)}\right) = \sin{\left(1 \right)}$$
$$\lim_{z \to \infty}\left(z \sin{\left(z \right)}\right) = \left\langle -\infty, \infty\right\rangle$$
More at z→oo
$$\lim_{z \to 0^-}\left(z \sin{\left(z \right)}\right) = 0$$
More at z→0 from the left
$$\lim_{z \to 0^+}\left(z \sin{\left(z \right)}\right) = 0$$
More at z→0 from the right
$$\lim_{z \to 1^-}\left(z \sin{\left(z \right)}\right) = \sin{\left(1 \right)}$$
More at z→1 from the left
$$\lim_{z \to 1^+}\left(z \sin{\left(z \right)}\right) = \sin{\left(1 \right)}$$
More at z→1 from the right
$$\lim_{z \to -\infty}\left(z \sin{\left(z \right)}\right) = \left\langle -\infty, \infty\right\rangle$$
More at z→-oo
More at z→-1 from the left
$$\lim_{z \to -1^+}\left(z \sin{\left(z \right)}\right) = \sin{\left(1 \right)}$$
$$\lim_{z \to \infty}\left(z \sin{\left(z \right)}\right) = \left\langle -\infty, \infty\right\rangle$$
More at z→oo
$$\lim_{z \to 0^-}\left(z \sin{\left(z \right)}\right) = 0$$
More at z→0 from the left
$$\lim_{z \to 0^+}\left(z \sin{\left(z \right)}\right) = 0$$
More at z→0 from the right
$$\lim_{z \to 1^-}\left(z \sin{\left(z \right)}\right) = \sin{\left(1 \right)}$$
More at z→1 from the left
$$\lim_{z \to 1^+}\left(z \sin{\left(z \right)}\right) = \sin{\left(1 \right)}$$
More at z→1 from the right
$$\lim_{z \to -\infty}\left(z \sin{\left(z \right)}\right) = \left\langle -\infty, \infty\right\rangle$$
More at z→-oo
One‐sided limits
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lim (z*sin(z)) z->-1+
$$\lim_{z \to -1^+}\left(z \sin{\left(z \right)}\right)$$
sin(1)
$$\sin{\left(1 \right)}$$
= 0.841470984807897
lim (z*sin(z)) z->-1-
$$\lim_{z \to -1^-}\left(z \sin{\left(z \right)}\right)$$
sin(1)
$$\sin{\left(1 \right)}$$
= 0.841470984807897
= 0.841470984807897
The graph