Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of -2+x^3+6*x
-
Limit of ((-2+x)/x)^(2*x)
-
Limit of (-2+x)*log(-2+x)
-
Limit of -6+x^2+5*x
-
Identical expressions
- (- two +x)*log(- two +x)
- ( minus 2 plus x) multiply by logarithm of ( minus 2 plus x)
- ( minus two plus x) multiply by logarithm of ( minus two plus x)
- (-2+x)log(-2+x)
- -2+xlog-2+x
-
Similar expressions
- (-2-x)*log(-2+x)
- (-2+x)*log(-2-x)
- (-2+x)*log(2+x)
- (2+x)*log(-2+x)
Limit of the function (-2+x)*log(-2+x)
The solution
You have entered
[src]
lim ((-2 + x)*log(-2 + x)) x->2+
$$\lim_{x \to 2^+}\left(\left(x - 2\right) \log{\left(x - 2 \right)}\right)$$
Limit((-2 + x)*log(-2 + x), x, 2)
The graph
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 2^-}\left(\left(x - 2\right) \log{\left(x - 2 \right)}\right) = 0$$
More at x→2 from the left
$$\lim_{x \to 2^+}\left(\left(x - 2\right) \log{\left(x - 2 \right)}\right) = 0$$
$$\lim_{x \to \infty}\left(\left(x - 2\right) \log{\left(x - 2 \right)}\right) = \infty$$
More at x→oo
$$\lim_{x \to 0^-}\left(\left(x - 2\right) \log{\left(x - 2 \right)}\right) = - 2 \log{\left(2 \right)} - 2 i \pi$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\left(x - 2\right) \log{\left(x - 2 \right)}\right) = - 2 \log{\left(2 \right)} - 2 i \pi$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\left(x - 2\right) \log{\left(x - 2 \right)}\right) = - i \pi$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\left(x - 2\right) \log{\left(x - 2 \right)}\right) = - i \pi$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\left(x - 2\right) \log{\left(x - 2 \right)}\right) = -\infty$$
More at x→-oo
More at x→2 from the left
$$\lim_{x \to 2^+}\left(\left(x - 2\right) \log{\left(x - 2 \right)}\right) = 0$$
$$\lim_{x \to \infty}\left(\left(x - 2\right) \log{\left(x - 2 \right)}\right) = \infty$$
More at x→oo
$$\lim_{x \to 0^-}\left(\left(x - 2\right) \log{\left(x - 2 \right)}\right) = - 2 \log{\left(2 \right)} - 2 i \pi$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\left(x - 2\right) \log{\left(x - 2 \right)}\right) = - 2 \log{\left(2 \right)} - 2 i \pi$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\left(x - 2\right) \log{\left(x - 2 \right)}\right) = - i \pi$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\left(x - 2\right) \log{\left(x - 2 \right)}\right) = - i \pi$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\left(x - 2\right) \log{\left(x - 2 \right)}\right) = -\infty$$
More at x→-oo
One‐sided limits
[src]
lim ((-2 + x)*log(-2 + x)) x->2+
$$\lim_{x \to 2^+}\left(\left(x - 2\right) \log{\left(x - 2 \right)}\right)$$
0
$$0$$
= -0.002013543998355
lim ((-2 + x)*log(-2 + x)) x->2-
$$\lim_{x \to 2^-}\left(\left(x - 2\right) \log{\left(x - 2 \right)}\right)$$
0
$$0$$
= (0.00193929632169612 - 0.00084074776060362j)
= (0.00193929632169612 - 0.00084074776060362j)
The graph