Mister Exam
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- Limit of the function:
-
Limit of 2^(-n)*2^(1+n)
- Limit of tan(k*x)/x
-
Limit of (-x+tan(x))/(x+2*sin(x))
-
Limit of asin(5*x)/tan(3*x)
- Integral of d{x}:
- log(sin(x))
- Derivative of:
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log(sin(x))
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Identical expressions
- log(sin(x))
- logarithm of ( sinus of (x))
- logsinx
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Similar expressions
- log(sin(x)/x)
- log(sin(x/2))/(1+cos(3*x))
- log(sinx)
Limit of the function log(sin(x))
The solution
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[src]
lim log(sin(x)) x->pi+
$$\lim_{x \to \pi^+} \log{\left(\sin{\left(x \right)} \right)}$$
Limit(log(sin(x)), x, pi)
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
One‐sided limits
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lim log(sin(x)) x->pi+
$$\lim_{x \to \pi^+} \log{\left(\sin{\left(x \right)} \right)}$$
-oo
$$-\infty$$
= (-8.84636960921524 + 3.14159265358979j)
lim log(sin(x)) x->pi-
$$\lim_{x \to \pi^-} \log{\left(\sin{\left(x \right)} \right)}$$
-oo
$$-\infty$$
= -8.84633718726286
= -8.84633718726286
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \pi^-} \log{\left(\sin{\left(x \right)} \right)} = -\infty$$
More at x→pi from the left
$$\lim_{x \to \pi^+} \log{\left(\sin{\left(x \right)} \right)} = -\infty$$
$$\lim_{x \to \infty} \log{\left(\sin{\left(x \right)} \right)} = \log{\left(\left\langle -1, 1\right\rangle \right)}$$
More at x→oo
$$\lim_{x \to 0^-} \log{\left(\sin{\left(x \right)} \right)} = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+} \log{\left(\sin{\left(x \right)} \right)} = -\infty$$
More at x→0 from the right
$$\lim_{x \to 1^-} \log{\left(\sin{\left(x \right)} \right)} = \log{\left(\sin{\left(1 \right)} \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \log{\left(\sin{\left(x \right)} \right)} = \log{\left(\sin{\left(1 \right)} \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \log{\left(\sin{\left(x \right)} \right)} = \log{\left(\left\langle -1, 1\right\rangle \right)}$$
More at x→-oo
More at x→pi from the left
$$\lim_{x \to \pi^+} \log{\left(\sin{\left(x \right)} \right)} = -\infty$$
$$\lim_{x \to \infty} \log{\left(\sin{\left(x \right)} \right)} = \log{\left(\left\langle -1, 1\right\rangle \right)}$$
More at x→oo
$$\lim_{x \to 0^-} \log{\left(\sin{\left(x \right)} \right)} = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+} \log{\left(\sin{\left(x \right)} \right)} = -\infty$$
More at x→0 from the right
$$\lim_{x \to 1^-} \log{\left(\sin{\left(x \right)} \right)} = \log{\left(\sin{\left(1 \right)} \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \log{\left(\sin{\left(x \right)} \right)} = \log{\left(\sin{\left(1 \right)} \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \log{\left(\sin{\left(x \right)} \right)} = \log{\left(\left\langle -1, 1\right\rangle \right)}$$
More at x→-oo
Numerical answer
[src]
(-8.84636960921524 + 3.14159265358979j)
(-8.84636960921524 + 3.14159265358979j)
The graph