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  • Evaluate: lim┬(x→1) ((x^7-2x^5+1)/(x^3-3x^2+2))

Evaluate:

\mathop{\lim }_{x \rightarrow 1} \left( \frac{x^{7}-2x^{5}+1}{x^{3}-3x^{2}+2} \right) \\ \\

Answers (1)

Let us apply LH rule i.e. L.Hospita'srule to this question  


  \\ ~~\mathop{\lim }_{x \rightarrow 1} \left( \frac{x^{7}-2x^{5}+1}{x^{3}-3x^{2}+2} \right) \\ \\ \mathop{\lim }_{x \rightarrow a} \left( \frac{f \left( x \right) }{g \left( x \right) } \right) =\mathop{\lim }_{x \rightarrow a} \left( \frac{f^{'} \left( x \right) }{g^{'} \left( x \right) } \right) \\ \\ \mathop{\lim }_{x \rightarrow 1} \left( \frac{x^{7}-2x^{5}+1}{x^{3}-3x^{2}+2} \right) =\mathop{\lim }_{x \rightarrow 1} \left( \frac{7x^{6}-10x^{4}}{3x^{2}-6x} \right) =\frac{7-10}{3-6}=1 \\ \\

 

Posted by

infoexpert21

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