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  • Evaluate, <img alt="\mathrm{\lim _{x \rightarrow 1}\left(\frac{1}{x-1}-\frac{3}{1-x^3}\right)}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%5Clim%20_%7Bx%20%5Crighta

Evaluate,

\mathrm{\lim _{x \rightarrow 1}\left(\frac{1}{x-1}-\frac{3}{1-x^3}\right)}

Option: 1

0


Option: 2

1


Option: 3

5


Option: 4

dose not exist


Answers (1)

best_answer

Using the identity \mathrm{A-B=\frac{1}{\frac{1}{A}}-\frac{1}{\frac{1}{B}}}  we get 
                        \mathrm{\frac{1}{x-1}-\frac{3}{1-x^3}=\frac{2-x^3-x}{-x^4+x^3+x-1}}
so you go from the from \mathrm{\infty-\infty} to the from \frac{0}{0} and you can L ' Hospital so you have 
                        \mathrm{\lim _{x \rightarrow 1} \frac{1}{x-1}-\frac{3}{1-x^3}=\lim \frac{-3 x^2-1}{-4 x^3+3 x^2+1}}
and you can verify that the limits to the right and to the lift are not equal, the first is \mathrm{-\infty} and the secondis \mathrm{\infty}.
Thus the limit does not exist

Posted by

HARSH KANKARIA

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