Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-6+x^2-x)/(6+x^2-5*x)
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Limit of log(1+x^2)/(-e^(-x)+cos(3*x))
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Limit of -2+|-2+x|/x
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Limit of (-4-8*x+8*x^2)/(3+8*x)
- Graphing y =:
- x*sin(1/x)
- Integral of d{x}:
- x*sin(1/x)
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Identical expressions
- x*sin(one /x)
- x multiply by sinus of (1 divide by x)
- x multiply by sinus of (one divide by x)
- xsin(1/x)
- xsin1/x
- x*sin(1 divide by x)
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Similar expressions
- sqrt(x)*sin(1/x)
- cos(x)*sin(1/x)
- x*sin(1/(x^2+y^2))
Limit of the function x*sin(1/x)
The solution
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[src]
/ /1\\ lim |x*sin|-|| x->0+\ \x//
$$\lim_{x \to 0^+}\left(x \sin{\left(\frac{1}{x} \right)}\right)$$
Limit(x*sin(1/x), x, 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
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-}\left(x \sin{\left(\frac{1}{x} \right)}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x \sin{\left(\frac{1}{x} \right)}\right) = 0$$
$$\lim_{x \to \infty}\left(x \sin{\left(\frac{1}{x} \right)}\right) = 1$$
More at x→oo
$$\lim_{x \to 1^-}\left(x \sin{\left(\frac{1}{x} \right)}\right) = \sin{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x \sin{\left(\frac{1}{x} \right)}\right) = \sin{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x \sin{\left(\frac{1}{x} \right)}\right) = 1$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x \sin{\left(\frac{1}{x} \right)}\right) = 0$$
$$\lim_{x \to \infty}\left(x \sin{\left(\frac{1}{x} \right)}\right) = 1$$
More at x→oo
$$\lim_{x \to 1^-}\left(x \sin{\left(\frac{1}{x} \right)}\right) = \sin{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x \sin{\left(\frac{1}{x} \right)}\right) = \sin{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x \sin{\left(\frac{1}{x} \right)}\right) = 1$$
More at x→-oo
One‐sided limits
[src]
/ /1\\ lim |x*sin|-|| x->0+\ \x//
$$\lim_{x \to 0^+}\left(x \sin{\left(\frac{1}{x} \right)}\right)$$
0
$$0$$
= 9.31999169637548e-21
/ /1\\ lim |x*sin|-|| x->0-\ \x//
$$\lim_{x \to 0^-}\left(x \sin{\left(\frac{1}{x} \right)}\right)$$
0
$$0$$
= 9.31999169637548e-21
= 9.31999169637548e-21
The graph