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-x)/(6+x^2-5*x)
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Limit of log(1+x^2)/(-e^(-x)+cos(3*x))
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Limit of -2+|-2+x|/x
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Limit of (-4-8*x+8*x^2)/(3+8*x)
- Derivative of:
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log(cos(2*x))
- Graphing y =:
- log(cos(2*x))
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Identical expressions
- log(cos(two *x))
- logarithm of ( co sinus of e of (2 multiply by x))
- logarithm of ( co sinus of e of (two multiply by x))
- log(cos(2x))
- logcos2x
Limit of the function log(cos(2*x))
The solution
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lim log(cos(2*x)) x->oo
$$\lim_{x \to \infty} \log{\left(\cos{\left(2 x \right)} \right)}$$
Limit(log(cos(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
$$\lim_{x \to \infty} \log{\left(\cos{\left(2 x \right)} \right)} = \log{\left(\left\langle -1, 1\right\rangle \right)}$$
$$\lim_{x \to 0^-} \log{\left(\cos{\left(2 x \right)} \right)} = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+} \log{\left(\cos{\left(2 x \right)} \right)} = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-} \log{\left(\cos{\left(2 x \right)} \right)} = \log{\left(- \cos{\left(2 \right)} \right)} + i \pi$$
More at x→1 from the left
$$\lim_{x \to 1^+} \log{\left(\cos{\left(2 x \right)} \right)} = \log{\left(- \cos{\left(2 \right)} \right)} + i \pi$$
More at x→1 from the right
$$\lim_{x \to -\infty} \log{\left(\cos{\left(2 x \right)} \right)} = \log{\left(\left\langle -1, 1\right\rangle \right)}$$
More at x→-oo
$$\lim_{x \to 0^-} \log{\left(\cos{\left(2 x \right)} \right)} = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+} \log{\left(\cos{\left(2 x \right)} \right)} = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-} \log{\left(\cos{\left(2 x \right)} \right)} = \log{\left(- \cos{\left(2 \right)} \right)} + i \pi$$
More at x→1 from the left
$$\lim_{x \to 1^+} \log{\left(\cos{\left(2 x \right)} \right)} = \log{\left(- \cos{\left(2 \right)} \right)} + i \pi$$
More at x→1 from the right
$$\lim_{x \to -\infty} \log{\left(\cos{\left(2 x \right)} \right)} = \log{\left(\left\langle -1, 1\right\rangle \right)}$$
More at x→-oo
The graph