F(x)=5+1/x
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x | 1 | 10 | 100 | 1000 | 10 000 | 100 000
f(x) | 6 | 5,1 | 5,01 | 5,001 | 5,0001 | 5,00001
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a=+∞ , f(x) ---> 5
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x | -1 | -10 | -100 | -1000 | -10 000 | -100 000
f(x) | 4 | 4,9 | 4,99 | 4,999 | 4,9999 | 4,99999
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a= -∞ , f(x) ---> 5
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x | 1,1 | 0,9 | 1,01 | 0,99 | 1,001 | 0,999
f(x) | 5,(90) | 6,(1) | 5,(9900) | 6,(01) | 5,(999000) | 6,(001)
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a=1 , f(x) ---> 6
![\lim\limits _{x \to +\infty} (5+\frac{1}{x})= 5\\\\ \lim\limits _{n\x \to -\infty} (5+\frac{1}{x})=5\\\\ \lim\limits _{x \to 1} (5+\frac{1}{x})=6](https://tex.z-dn.net/?f=+%5Clim%5Climits+_%7Bx+%5Cto+%2B%5Cinfty%7D+%285%2B%5Cfrac%7B1%7D%7Bx%7D%29%3D+5%5C%5C%5C%5C+%5Clim%5Climits+_%7Bn%5Cx+%5Cto+-%5Cinfty%7D+%285%2B%5Cfrac%7B1%7D%7Bx%7D%29%3D5%5C%5C%5C%5C+%5Clim%5Climits+_%7Bx+%5Cto+1%7D+%285%2B%5Cfrac%7B1%7D%7Bx%7D%29%3D6)