Mister Exam
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How to use it?
- Limit of the function:
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Limit of (-16+x^2-6*x)/(-2+x+x^2)
-
Limit of -1+sqrt(5)-x-2/(sqrt(2)-x)
- Limit of (-log(-1+2*x)+log(2+x))/sin(pi*x)
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Limit of (-1+log(x))/(-1+e)
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Identical expressions
- (- one +log(x))/(- one +e)
- ( minus 1 plus logarithm of (x)) divide by ( minus 1 plus e)
- ( minus one plus logarithm of (x)) divide by ( minus one plus e)
- -1+logx/-1+e
- (-1+log(x)) divide by (-1+e)
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Similar expressions
- (-1+log(x))/(-1+exp(x))
- (-1+log(x))/(1+e)
- (1+log(x))/(-1+e)
- (-1-log(x))/(-1+e)
- (-1+log(x))/(-1-e)
Limit of the function (-1+log(x))/(-1+e)
The solution
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[src]
/-1 + log(x)\ lim |-----------| x->E+\ -1 + E /
$$\lim_{x \to e^+}\left(\frac{\log{\left(x \right)} - 1}{-1 + e}\right)$$
Limit((-1 + log(x))/(-1 + E), x, E)
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
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/-1 + log(x)\ lim |-----------| x->E+\ -1 + E /
$$\lim_{x \to e^+}\left(\frac{\log{\left(x \right)} - 1}{-1 + e}\right)$$
0
$$0$$
= -3.09509046683877e-17
/-1 + log(x)\ lim |-----------| x->E-\ -1 + E /
$$\lim_{x \to e^-}\left(\frac{\log{\left(x \right)} - 1}{-1 + e}\right)$$
0
$$0$$
= -3.09509046683878e-17
= -3.09509046683878e-17
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to e^-}\left(\frac{\log{\left(x \right)} - 1}{-1 + e}\right) = 0$$
More at x→E from the left
$$\lim_{x \to e^+}\left(\frac{\log{\left(x \right)} - 1}{-1 + e}\right) = 0$$
$$\lim_{x \to \infty}\left(\frac{\log{\left(x \right)} - 1}{-1 + e}\right) = \infty$$
More at x→oo
$$\lim_{x \to 0^-}\left(\frac{\log{\left(x \right)} - 1}{-1 + e}\right) = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\log{\left(x \right)} - 1}{-1 + e}\right) = -\infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{\log{\left(x \right)} - 1}{-1 + e}\right) = - \frac{1}{-1 + e}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\log{\left(x \right)} - 1}{-1 + e}\right) = - \frac{1}{-1 + e}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\log{\left(x \right)} - 1}{-1 + e}\right) = \infty$$
More at x→-oo
More at x→E from the left
$$\lim_{x \to e^+}\left(\frac{\log{\left(x \right)} - 1}{-1 + e}\right) = 0$$
$$\lim_{x \to \infty}\left(\frac{\log{\left(x \right)} - 1}{-1 + e}\right) = \infty$$
More at x→oo
$$\lim_{x \to 0^-}\left(\frac{\log{\left(x \right)} - 1}{-1 + e}\right) = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\log{\left(x \right)} - 1}{-1 + e}\right) = -\infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{\log{\left(x \right)} - 1}{-1 + e}\right) = - \frac{1}{-1 + e}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\log{\left(x \right)} - 1}{-1 + e}\right) = - \frac{1}{-1 + e}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\log{\left(x \right)} - 1}{-1 + e}\right) = \infty$$
More at x→-oo
The graph