Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-cos(5*x)+cos(3*x))/x^2
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Limit of (-12+x+x^2)/(-9+x^2)
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Limit of (2+x^2+3*x)/(3+x^2+4*x)
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Limit of (1-cos(x))/(x-sin(x))
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Identical expressions
- log(x)/(one + two *log(x)*sin(x))
- logarithm of (x) divide by (1 plus 2 multiply by logarithm of (x) multiply by sinus of (x))
- logarithm of (x) divide by (one plus two multiply by logarithm of (x) multiply by sinus of (x))
- log(x)/(1+2log(x)sin(x))
- logx/1+2logxsinx
- log(x) divide by (1+2*log(x)*sin(x))
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Similar expressions
- log(x)/(1-2*log(x)*sin(x))
- log(x)/(1+2*log(x)*sinx)
Limit of the function log(x)/(1+2*log(x)*sin(x))
The solution
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[src]
/ log(x) \ lim |-------------------| x->0+\1 + 2*log(x)*sin(x)/
$$\lim_{x \to 0^+}\left(\frac{\log{\left(x \right)}}{2 \log{\left(x \right)} \sin{\left(x \right)} + 1}\right)$$
Limit(log(x)/(1 + (2*log(x))*sin(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
One‐sided limits
[src]
/ log(x) \ lim |-------------------| x->0+\1 + 2*log(x)*sin(x)/
$$\lim_{x \to 0^+}\left(\frac{\log{\left(x \right)}}{2 \log{\left(x \right)} \sin{\left(x \right)} + 1}\right)$$
-oo
$$-\infty$$
= -5.37442978504336
/ log(x) \ lim |-------------------| x->0-\1 + 2*log(x)*sin(x)/
$$\lim_{x \to 0^-}\left(\frac{\log{\left(x \right)}}{2 \log{\left(x \right)} \sin{\left(x \right)} + 1}\right)$$
-oo
$$-\infty$$
= (-8.83238964783365 + 3.08716177900752j)
= (-8.83238964783365 + 3.08716177900752j)
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-}\left(\frac{\log{\left(x \right)}}{2 \log{\left(x \right)} \sin{\left(x \right)} + 1}\right) = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\log{\left(x \right)}}{2 \log{\left(x \right)} \sin{\left(x \right)} + 1}\right) = -\infty$$
$$\lim_{x \to \infty}\left(\frac{\log{\left(x \right)}}{2 \log{\left(x \right)} \sin{\left(x \right)} + 1}\right)$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{\log{\left(x \right)}}{2 \log{\left(x \right)} \sin{\left(x \right)} + 1}\right) = 0$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\log{\left(x \right)}}{2 \log{\left(x \right)} \sin{\left(x \right)} + 1}\right) = 0$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\log{\left(x \right)}}{2 \log{\left(x \right)} \sin{\left(x \right)} + 1}\right)$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\log{\left(x \right)}}{2 \log{\left(x \right)} \sin{\left(x \right)} + 1}\right) = -\infty$$
$$\lim_{x \to \infty}\left(\frac{\log{\left(x \right)}}{2 \log{\left(x \right)} \sin{\left(x \right)} + 1}\right)$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{\log{\left(x \right)}}{2 \log{\left(x \right)} \sin{\left(x \right)} + 1}\right) = 0$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\log{\left(x \right)}}{2 \log{\left(x \right)} \sin{\left(x \right)} + 1}\right) = 0$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\log{\left(x \right)}}{2 \log{\left(x \right)} \sin{\left(x \right)} + 1}\right)$$
More at x→-oo
The graph