Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (4+x^7-2*x^5)/(6+x^2+2*x^5)
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Limit of ((6+x)/(4+x))^(1+x)
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Limit of (-6+x)/(3+sqrt(3+x))
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Limit of (8+x^4+6*x)/(-7+2*x^4+3*x^2)
- Derivative of:
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x^2*log(2*x)
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Identical expressions
- x^ two *log(two *x)
- x squared multiply by logarithm of (2 multiply by x)
- x to the power of two multiply by logarithm of (two multiply by x)
- x2*log(2*x)
- x2*log2*x
- x²*log(2*x)
- x to the power of 2*log(2*x)
- x^2log(2x)
- x2log(2x)
- x2log2x
- x^2log2x
Limit of the function x^2*log(2*x)
The solution
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[src]
/ 2 \ lim \x *log(2*x)/ x->0+
$$\lim_{x \to 0^+}\left(x^{2} \log{\left(2 x \right)}\right)$$
Limit(x^2*log(2*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
$$\lim_{x \to 0^-}\left(x^{2} \log{\left(2 x \right)}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x^{2} \log{\left(2 x \right)}\right) = 0$$
$$\lim_{x \to \infty}\left(x^{2} \log{\left(2 x \right)}\right) = \infty$$
More at x→oo
$$\lim_{x \to 1^-}\left(x^{2} \log{\left(2 x \right)}\right) = \log{\left(2 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x^{2} \log{\left(2 x \right)}\right) = \log{\left(2 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x^{2} \log{\left(2 x \right)}\right) = \infty$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x^{2} \log{\left(2 x \right)}\right) = 0$$
$$\lim_{x \to \infty}\left(x^{2} \log{\left(2 x \right)}\right) = \infty$$
More at x→oo
$$\lim_{x \to 1^-}\left(x^{2} \log{\left(2 x \right)}\right) = \log{\left(2 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x^{2} \log{\left(2 x \right)}\right) = \log{\left(2 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x^{2} \log{\left(2 x \right)}\right) = \infty$$
More at x→-oo
One‐sided limits
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/ 2 \ lim \x *log(2*x)/ x->0+
$$\lim_{x \to 0^+}\left(x^{2} \log{\left(2 x \right)}\right)$$
0
$$0$$
= -7.10650090666474e-7
/ 2 \ lim \x *log(2*x)/ x->0-
$$\lim_{x \to 0^-}\left(x^{2} \log{\left(2 x \right)}\right)$$
0
$$0$$
= (-7.38794385802473e-7 + 3.52411446919995e-7j)
= (-7.38794385802473e-7 + 3.52411446919995e-7j)
The graph