Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (1+3*x)^(5/x)
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Limit of x^2/(-2+sqrt(4+x^2))
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Limit of ((5+x^2-6*x)/(5+x^2-5*x))^(2+3*x)
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Limit of (2+x^2+3*x)/(-4+x^2)
- Derivative of:
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log(cos(x))
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Identical expressions
- log(cos(x))
- logarithm of ( co sinus of e of (x))
- logcosx
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Similar expressions
- x*log(cos(x/2))
- log(cos(x/2))/sin(x)
- log(cosx)
Limit of the function log(cos(x))
The solution
You have entered
[src]
lim log(cos(x)) x->0+
$$\lim_{x \to 0^+} \log{\left(\cos{\left(x \right)} \right)}$$
Limit(log(cos(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
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-} \log{\left(\cos{\left(x \right)} \right)} = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+} \log{\left(\cos{\left(x \right)} \right)} = 0$$
$$\lim_{x \to \infty} \log{\left(\cos{\left(x \right)} \right)} = \log{\left(\left\langle -1, 1\right\rangle \right)}$$
More at x→oo
$$\lim_{x \to 1^-} \log{\left(\cos{\left(x \right)} \right)} = \log{\left(\cos{\left(1 \right)} \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \log{\left(\cos{\left(x \right)} \right)} = \log{\left(\cos{\left(1 \right)} \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \log{\left(\cos{\left(x \right)} \right)} = \log{\left(\left\langle -1, 1\right\rangle \right)}$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+} \log{\left(\cos{\left(x \right)} \right)} = 0$$
$$\lim_{x \to \infty} \log{\left(\cos{\left(x \right)} \right)} = \log{\left(\left\langle -1, 1\right\rangle \right)}$$
More at x→oo
$$\lim_{x \to 1^-} \log{\left(\cos{\left(x \right)} \right)} = \log{\left(\cos{\left(1 \right)} \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \log{\left(\cos{\left(x \right)} \right)} = \log{\left(\cos{\left(1 \right)} \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \log{\left(\cos{\left(x \right)} \right)} = \log{\left(\left\langle -1, 1\right\rangle \right)}$$
More at x→-oo
One‐sided limits
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lim log(cos(x)) x->0+
$$\lim_{x \to 0^+} \log{\left(\cos{\left(x \right)} \right)}$$
0
$$0$$
= 4.87919127836376e-31
lim log(cos(x)) x->0-
$$\lim_{x \to 0^-} \log{\left(\cos{\left(x \right)} \right)}$$
0
$$0$$
= 4.87919127836376e-31
= 4.87919127836376e-31
The graph