Limit of x^2*(1-ln(x+1))/(sin(x)-x) when x -> 0

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ID	Problem	Count
1	$$ \lim\limits_{x \to 0+} ~ -x{\cdot}\ln\left(x\right) $$	689
2	$$ \lim\limits_{x \to 0} ~ \cos\left(\dfrac{2{\pi}{\cdot}x-{\pi}{\cdot}\sin\left(x\right)}{2x+\sin\left(x\right)}\right) $$	325
3	$$ limlimits_{x to 0+} ~ -x{cdot}lnleft(xright) $$	141
4	$$ %5clim%5climits_%7bx %5cto 0%7d ~ %5ccos%5cleft(%5cdfrac%7b2%7b%5cpi%7d%7b%5ccdot%7dx-%7b%5cpi%7d%7b%5ccdot%7d%5csin%5cleft(x%5cright)%7d%7b2x+%5csin%5cleft(x%5cright)%7d%5cright) $$	128
5	$$ %5clim%5climits_%7bx %5cto 0+%7d ~ -x%7b%5ccdot%7d%5cln%5cleft(x%5cright) $$	91
6	$$ \lim\limits_{x \to \infty} ~ {\left(1+\dfrac{1}{x}\right)}^{x} $$	85
7	$$ \lim\limits_{x \to \infty} ~ {2}^{-x}+3 $$	39
8	$$ \lim\limits_{x \to 1} ~ \dfrac{{x}^{2}+3x-4}{x-1} $$	36
9	$$ %5clim%5climits_%7bx %5cto -5%7d ~ %5cdfrac%7b5x-25%7d%7bx+5%7d $$	29
10	$$ \lim\limits_{x \to 3-} ~ \dfrac{{x}^{2}+4}{x-3} $$	25
11	$$ \lim\limits_{x \to 3} ~ \sqrt{{x}^{2}+7}+5 $$	22
12	$$ \lim\limits_{x \to 0} ~ \cos\left(\dfsqrtac{2{\pi}{\cdot}x-{\pi}{\cdot}\sin\left(x\sqrtight)}{2x \sin\left(x\sqrtight)}\sqrtight) $$	21
13	$$ \lim\limits_{x \to -5} ~ \dfrac{5x-25}{x+5} $$	20
14	$$ \lim\limits_{x \to 2} ~ \dfrac{\sin\left({x}^{2}-4\right)}{x-2} $$	17
15	$$ \lim\limits_{x \to 0} ~ \dfrac{\tan\left(7\right){\cdot}x}{3}{\cdot}x $$	13
16	$$ \lim\limits_{x \to 0} ~ \dfrac{\sin\left(x\right)}{x} $$	12
17	$$ \lim\limits_{x \to -1} ~ \dfrac{{x}^{3}+{x}^{2}-x-1}{{x}^{3}+{x}^{2}+x+1} $$	12
18	$$ \lim\limits_{x \to 0} ~ \sin\left(x\right){\cdot}\sin\left(\dfrac{1}{x}\right) $$	12
19	$$ \lim\limits_{x \to \infty} ~ \dfrac{2x+\tan\left(x\right)}{3x+\cot\left(x\right)} $$	12
20	$$ \lim\limits_{x \to 0} ~ \cos\left(\dfrac{2{\pi}{\cdot}x-{\pi}{\cdot}\sin\left(x\right)}{2x+\sin\left(x\right)}\right) $$	11
21	$$ \lim\limits_{x \to 0} ~ \dfrac{{x}^{2}{\cdot}\left(1-\ln\left(x+1\right)\right)}{\sin\left(x\right)-x} $$	11
22	$$ \lim\limits_{x \to \pi/2-} ~ {\left(1+\cos\left(x\right)\right)}^{\tan\left(x\right)} $$	10
23	$$ \lim\limits_{x \to 0} ~ {x}^{x} $$	10
24	$$ \lim\limits_{x \to \infty+} ~ \dfrac{-2{x}^{2}+x-1}{3x-1} $$	10
25	$$ \lim\limits_{x \to 1} ~ 3{x}^{2}-1 $$	10
26	$$ \lim\limits_{x \to 0} ~ \dfrac{\sin\left(x\right)+\cos\left(x\right)-1}{x} $$	10
27	$$ \lim\limits_{x \to 4} ~ \dfrac{\sqrt{{x}^{2}-7}-3}{x-4} $$	10
28	$$ \lim\limits_{x \to \infty} ~ \dfrac{9{x}^{2}+5x}{3{x}^{2}+x+5} $$	10
29	$$ \lim\limits_{x \to \infty} ~ \dfrac{3{x}^{4}+5{x}^{2}+2}{4{x}^{3}+5x+2} $$	9
30	$$ \lim\limits_{x \to 0} ~ \sin\left(x\right) $$	9
31	$$ \lim\limits_{x \to \infty} ~ \dfrac{5{x}^{3}+3{x}^{2}+8}{\left(x-1\right){\cdot}\left(3{x}^{2}+1\right)} $$	9
32	$$ \lim\limits_{x \to 1+} ~ \sqrt{{x}^{2}-4x+3} $$	9
33	$$ \lim\limits_{x \to 2} ~ \dfrac{{x}^{3}-8}{2x-4} $$	9
34	$$ \lim\limits_{x \to 1} ~ \dfrac{{x}^{2}-5x+4}{{x}^{2}+2x-3} $$	9
35	$$ \lim\limits_{x \to -2} ~ \dfrac{{x}^{3}+8}{{x}^{2}-4} $$	8
36	$$ \lim\limits_{x \to 0} ~ \dfrac{x+\tan\left(x\right)}{\sin\left(3\right){\cdot}x} $$	8
37	$$ \lim\limits_{x \to 4} ~ \dfrac{4x-{x}^{2}}{2-\sqrt{x}} $$	8
38	$$ \lim\limits_{x \to 2+} ~ {4}^{{2}^{x}}-32{\cdot}{4}^{x}+256 $$	8
39	$$ \lim\limits_{x \to \infty} ~ \dfrac{x+3}{4{x}^{2}+x+1} $$	8
40	$$ \lim\limits_{x \to \infty-} ~ \sqrt{4{x}^{2}-3x+1}+2x $$	8
41	$$ \lim\limits_{x \to 0} ~ x{\cdot}\ln\left(x\right) $$	7
42	$$ \lim\limits_{x \to \infty} ~ \dfrac{1}{x} $$	7
43	$$ \lim\limits_{x+\to+0}+~+\cos\left(\dfrac{2{\pi}{\cdot}x-{\pi}{\cdot}\sin\left(x\right)}{2x+\sin\left(x\right)}\right) $$	7
44	$$ \lim\limits_{x \to 0} ~ \dfrac{1-\cos\left(x\right)}{{x}^{2}} $$	7
45	$$ \lim\limits_{x \to 0} ~ {x}^{2}{\cdot}\dfrac{1}{x} $$	7
46	$$ \lim\limits_{x \to -0.1} ~ \dfrac{6{\cdot}\sin\left(x\right)}{x} $$	7
47	$$ \lim\limits_{x \to 0.01} ~ \dfrac{6{\cdot}\sin\left(x\right)}{x} $$	7
48	$$ \lim\limits_{x \to 0+} ~ \dfrac{\sin\left(x\right)+\cos\left(x\right)-1}{x} $$	7
49	$$ \lim\limits_{x \to 1+} ~ \dfrac{{x}^{2}-1}{x-1} $$	7
50	$$ \lim\limits_{x \to 0} ~ \dfrac{1}{x} $$	6

Problem

Count

$$ \lim\limits_{x \to 0+} ~ -x{\cdot}\ln\left(x\right) $$

689

$$ \lim\limits_{x \to 0} ~ \cos\left(\dfrac{2{\pi}{\cdot}x-{\pi}{\cdot}\sin\left(x\right)}{2x+\sin\left(x\right)}\right) $$

325

$$ limlimits_{x to 0+} ~ -x{cdot}lnleft(xright) $$

141

$$ %5clim%5climits_%7bx %5cto 0%7d ~ %5ccos%5cleft(%5cdfrac%7b2%7b%5cpi%7d%7b%5ccdot%7dx-%7b%5cpi%7d%7b%5ccdot%7d%5csin%5cleft(x%5cright)%7d%7b2x+%5csin%5cleft(x%5cright)%7d%5cright) $$

128

$$ %5clim%5climits_%7bx %5cto 0+%7d ~ -x%7b%5ccdot%7d%5cln%5cleft(x%5cright) $$

$$ \lim\limits_{x \to \infty} ~ {\left(1+\dfrac{1}{x}\right)}^{x} $$