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  • <img alt="\lim_{x\rightarrow 7/2}\frac{2x^{2}-9x+7}{2x^{2}-5x-7}" src="https://learn.careers360.com/latex-image/?%5Clim_%7Bx%5Crightarrow%207/2%7D%5Cfrac%7B2x%5E%7B2%7D-9x&plus;7%7D%7B2x%5E%7B2

\lim_{x\rightarrow 7/2}\frac{2x^{2}-9x+7}{2x^{2}-5x-7}  equals

Option: 1

4/9


Option: 2

5/9


Option: 3

2/3


Option: 4

7/9


Answers (1)

best_answer

As we have learned

 

Method of factorisation -

 Indeterminate\:form\:of\:\frac{0}{0}\:and \:\frac{\infty }{\infty }

We remove the denominator factor which it makes zero.


\lim_{x\rightarrow 1}\:\frac{x^{2}-1}{x-1}=\lim_{x\rightarrow 1}=\frac{(x-1)(x+1)}{(x-1)}=1+1=2

 

- wherein

\frac{0}{finite}=0


\frac{finite}{0}=\infty

 

  

\lim_{x\rightarrow 7/2} \frac{2x^2-9x+7}{2x^2-5x-7}= \lim_{x\rightarrow 7/2}\frac{(2x-7)(x-1)}{(2x-7)(x+1)}

= \lim_{x\rightarrow 7/2}\frac{x-1}{x+1}= \frac{5/2}{9/2}= \frac{5}{9}

 

 

 

 

Posted by

himanshu.meshram

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