Mister Exam
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How to use it?
- Limit of the function:
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Limit of (-exp(-x)+exp(x))/(exp(x)+exp(-x))
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Limit of ((3+5*x)/(-2+4*x))^(1+3*x)
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Limit of (3+3*x^3+5*x+5*x^2)/(-1+x^2)
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Limit of (3-x^2+5*x)/(4*x^7+81*x)
- Derivative of:
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log(x^2+2*x)
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Identical expressions
- log(x^ two + two *x)
- logarithm of (x squared plus 2 multiply by x)
- logarithm of (x to the power of two plus two multiply by x)
- log(x2+2*x)
- logx2+2*x
- log(x²+2*x)
- log(x to the power of 2+2*x)
- log(x^2+2x)
- log(x2+2x)
- logx2+2x
- logx^2+2x
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Similar expressions
- log(x^2-2*x)
Limit of the function log(x^2+2*x)
The solution
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[src]
/ 2 \ lim log\x + 2*x/ x->0+
$$\lim_{x \to 0^+} \log{\left(x^{2} + 2 x \right)}$$
Limit(log(x^2 + 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
One‐sided limits
[src]
/ 2 \ lim log\x + 2*x/ x->0+
$$\lim_{x \to 0^+} \log{\left(x^{2} + 2 x \right)}$$
-oo
$$-\infty$$
= -8.19804051398379
/ 2 \ lim log\x + 2*x/ x->0-
$$\lim_{x \to 0^-} \log{\left(x^{2} + 2 x \right)}$$
-oo
$$-\infty$$
= (-8.18273783923912 + 3.14159265358979j)
= (-8.18273783923912 + 3.14159265358979j)
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-} \log{\left(x^{2} + 2 x \right)} = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+} \log{\left(x^{2} + 2 x \right)} = -\infty$$
$$\lim_{x \to \infty} \log{\left(x^{2} + 2 x \right)} = \infty$$
More at x→oo
$$\lim_{x \to 1^-} \log{\left(x^{2} + 2 x \right)} = \log{\left(3 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \log{\left(x^{2} + 2 x \right)} = \log{\left(3 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \log{\left(x^{2} + 2 x \right)} = \infty$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+} \log{\left(x^{2} + 2 x \right)} = -\infty$$
$$\lim_{x \to \infty} \log{\left(x^{2} + 2 x \right)} = \infty$$
More at x→oo
$$\lim_{x \to 1^-} \log{\left(x^{2} + 2 x \right)} = \log{\left(3 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \log{\left(x^{2} + 2 x \right)} = \log{\left(3 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \log{\left(x^{2} + 2 x \right)} = \infty$$
More at x→-oo