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Aleks04 [339]
3 years ago
9

Find the limit of the function algebraically.

Mathematics
1 answer:
ArbitrLikvidat [17]3 years ago
5 0
\bf \lim\limits_{x\to -10}~\cfrac{x^2-100}{x+10}\implies \cfrac{\stackrel{\textit{difference of squares}}{x^2-10^2}}{x+10}\implies \cfrac{(x-10)(\underline{x+10})}{\underline{x+10}}
\\\\\\
\lim\limits_{x\to -10}~x-10\implies \lim\limits_{x\to -10}~-10-10\implies -20
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Step-by-step explanation:

Step-1 : Multiply the coefficient of the first term by the constant   1 • -56 = -56  

Step-2 : Find two factors of  -56  whose sum equals the coefficient of the middle term, which is   -10 .

     -56    +    1    =    -55  

     -28    +    2    =    -26  

     -14    +    4    =    -10    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -14  and  4  

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Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (x-14)

             Add up the last 2 terms, pulling out common factors :

                   4 • (x-14)

Step-5 : Add up the four terms of step 4 :

                   (x+4)  •  (x-14)

            Which is the desired factorization

Equation at the end of step  1  :

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