Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of 10+x^2+3*x^3+8*x
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Limit of (-2+sqrt(x))/(-4+x^2)
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Limit of x+2*x^3+5*x^4-x^2/3
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Limit of (-x^3+2*x+5*x^4)/(1+x^4-8*x^3)
- Derivative of:
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cos(x)/log(x)
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Identical expressions
- cos(x)/log(x)
- co sinus of e of (x) divide by logarithm of (x)
- cosx/logx
- cos(x) divide by log(x)
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Similar expressions
- (-1+x^cos(x))/(log(x)*sin(x))
- (-1+cos(x))/log(x)
- cosx/log(x)
Limit of the function cos(x)/log(x)
The solution
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/cos(x)\ lim |------| x->oo\log(x)/
$$\lim_{x \to \infty}\left(\frac{\cos{\left(x \right)}}{\log{\left(x \right)}}\right)$$
Limit(cos(x)/log(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
$$\lim_{x \to \infty}\left(\frac{\cos{\left(x \right)}}{\log{\left(x \right)}}\right) = 0$$
$$\lim_{x \to 0^-}\left(\frac{\cos{\left(x \right)}}{\log{\left(x \right)}}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\cos{\left(x \right)}}{\log{\left(x \right)}}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{\cos{\left(x \right)}}{\log{\left(x \right)}}\right) = -\infty$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\cos{\left(x \right)}}{\log{\left(x \right)}}\right) = \infty$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\cos{\left(x \right)}}{\log{\left(x \right)}}\right) = 0$$
More at x→-oo
$$\lim_{x \to 0^-}\left(\frac{\cos{\left(x \right)}}{\log{\left(x \right)}}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\cos{\left(x \right)}}{\log{\left(x \right)}}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{\cos{\left(x \right)}}{\log{\left(x \right)}}\right) = -\infty$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\cos{\left(x \right)}}{\log{\left(x \right)}}\right) = \infty$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\cos{\left(x \right)}}{\log{\left(x \right)}}\right) = 0$$
More at x→-oo
The graph