Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (1+x^2+9*x)/(-5+2*x+7*x^2)
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Limit of ((5+x^2-6*x)/(5+x^2-5*x))^(2+3*x)
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Limit of (2+x^2+3*x)/(-4+x^2)
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Limit of (-8+x^2+2*x)/(-2+x)
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Identical expressions
- log(one -x^ three)
- logarithm of (1 minus x cubed )
- logarithm of (one minus x to the power of three)
- log(1-x3)
- log1-x3
- log(1-x³)
- log(1-x to the power of 3)
- log1-x^3
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Similar expressions
- log(1+x^3)
Limit of the function log(1-x^3)
The solution
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[src]
/ 3\ lim log\1 - x / x->0+
$$\lim_{x \to 0^+} \log{\left(1 - x^{3} \right)}$$
Limit(log(1 - x^3), 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
$$\lim_{x \to 0^-} \log{\left(1 - x^{3} \right)} = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+} \log{\left(1 - x^{3} \right)} = 0$$
$$\lim_{x \to \infty} \log{\left(1 - x^{3} \right)} = \infty$$
More at x→oo
$$\lim_{x \to 1^-} \log{\left(1 - x^{3} \right)} = -\infty$$
More at x→1 from the left
$$\lim_{x \to 1^+} \log{\left(1 - x^{3} \right)} = -\infty$$
More at x→1 from the right
$$\lim_{x \to -\infty} \log{\left(1 - x^{3} \right)} = \infty$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+} \log{\left(1 - x^{3} \right)} = 0$$
$$\lim_{x \to \infty} \log{\left(1 - x^{3} \right)} = \infty$$
More at x→oo
$$\lim_{x \to 1^-} \log{\left(1 - x^{3} \right)} = -\infty$$
More at x→1 from the left
$$\lim_{x \to 1^+} \log{\left(1 - x^{3} \right)} = -\infty$$
More at x→1 from the right
$$\lim_{x \to -\infty} \log{\left(1 - x^{3} \right)} = \infty$$
More at x→-oo
One‐sided limits
[src]
/ 3\ lim log\1 - x / x->0+
$$\lim_{x \to 0^+} \log{\left(1 - x^{3} \right)}$$
0
$$0$$
= 8.60695006741856e-32
/ 3\ lim log\1 - x / x->0-
$$\lim_{x \to 0^-} \log{\left(1 - x^{3} \right)}$$
0
$$0$$
= 9.54149910004164e-30
= 9.54149910004164e-30
The graph