Mister Exam
Other calculators:
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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)
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Limit of -1+sqrt(5)-x-2/(sqrt(2)-x)
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Limit of (e^x-x-cos(x))/(-x+log(1+x))
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Limit of (-cos(x)^3+cos(x))/(4*x*sin(x))
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Identical expressions
- log(five *x)^(one /log(two *x))
- logarithm of (5 multiply by x) to the power of (1 divide by logarithm of (2 multiply by x))
- logarithm of (five multiply by x) to the power of (one divide by logarithm of (two multiply by x))
- log(5*x)(1/log(2*x))
- log5*x1/log2*x
- log(5x)^(1/log(2x))
- log(5x)(1/log(2x))
- log5x1/log2x
- log5x^1/log2x
- log(5*x)^(1 divide by log(2*x))
Limit of the function log(5*x)^(1/log(2*x))
The solution
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[src]
1
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log(2*x)
lim (log(5*x))
x->oo
$$\lim_{x \to \infty} \log{\left(5 x \right)}^{\frac{1}{\log{\left(2 x \right)}}}$$
Limit(log(5*x)^(1/log(2*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
$$\lim_{x \to \infty} \log{\left(5 x \right)}^{\frac{1}{\log{\left(2 x \right)}}} = 1$$
$$\lim_{x \to 0^-} \log{\left(5 x \right)}^{\frac{1}{\log{\left(2 x \right)}}} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} \log{\left(5 x \right)}^{\frac{1}{\log{\left(2 x \right)}}} = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-} \log{\left(5 x \right)}^{\frac{1}{\log{\left(2 x \right)}}} = \log{\left(5 \right)}^{\frac{1}{\log{\left(2 \right)}}}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \log{\left(5 x \right)}^{\frac{1}{\log{\left(2 x \right)}}} = \log{\left(5 \right)}^{\frac{1}{\log{\left(2 \right)}}}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \log{\left(5 x \right)}^{\frac{1}{\log{\left(2 x \right)}}} = 1$$
More at x→-oo
$$\lim_{x \to 0^-} \log{\left(5 x \right)}^{\frac{1}{\log{\left(2 x \right)}}} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} \log{\left(5 x \right)}^{\frac{1}{\log{\left(2 x \right)}}} = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-} \log{\left(5 x \right)}^{\frac{1}{\log{\left(2 x \right)}}} = \log{\left(5 \right)}^{\frac{1}{\log{\left(2 \right)}}}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \log{\left(5 x \right)}^{\frac{1}{\log{\left(2 x \right)}}} = \log{\left(5 \right)}^{\frac{1}{\log{\left(2 \right)}}}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \log{\left(5 x \right)}^{\frac{1}{\log{\left(2 x \right)}}} = 1$$
More at x→-oo
The graph