Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (6+x^2+2*x)/(-1+3*x^2+7*x)
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Limit of (4+5*x^2+7*x)/(7-3*x+8*x^2)
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Limit of (1-2*x+5*x^2)/(-3+x+2*x^2)
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Limit of 4/(9*x)
- Derivative of:
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log(sqrt(x))
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Identical expressions
- log(sqrt(x))
- logarithm of ( square root of (x))
- log(√(x))
- logsqrtx
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Similar expressions
- log(sqrt(x^2+3*x))/sqrt(x^2-x)
- log(sqrt(x^2-x))/(x^2-x)
Limit of the function log(sqrt(x))
The solution
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/ ___\ lim log\\/ x / x->oo
$$\lim_{x \to \infty} \log{\left(\sqrt{x} \right)}$$
Limit(log(sqrt(x)), x, oo, dir='-')
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
$$\lim_{x \to \infty} \log{\left(\sqrt{x} \right)} = \infty$$
$$\lim_{x \to 0^-} \log{\left(\sqrt{x} \right)} = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+} \log{\left(\sqrt{x} \right)} = -\infty$$
More at x→0 from the right
$$\lim_{x \to 1^-} \log{\left(\sqrt{x} \right)} = 0$$
More at x→1 from the left
$$\lim_{x \to 1^+} \log{\left(\sqrt{x} \right)} = 0$$
More at x→1 from the right
$$\lim_{x \to -\infty} \log{\left(\sqrt{x} \right)} = \infty$$
More at x→-oo
$$\lim_{x \to 0^-} \log{\left(\sqrt{x} \right)} = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+} \log{\left(\sqrt{x} \right)} = -\infty$$
More at x→0 from the right
$$\lim_{x \to 1^-} \log{\left(\sqrt{x} \right)} = 0$$
More at x→1 from the left
$$\lim_{x \to 1^+} \log{\left(\sqrt{x} \right)} = 0$$
More at x→1 from the right
$$\lim_{x \to -\infty} \log{\left(\sqrt{x} \right)} = \infty$$
More at x→-oo
The graph