Find the limit of the function algebraically.

limit as x approaches nine of quantity x squared minus eighty one divided by quantity x minus nine.

Question

Find the limit of the function algebraically.

limit as x approaches nine of quantity x squared minus eighty one divided by quantity x minus nine.

campbell_st · Answer

so the problem looks like 

$$\lim_{x \rightarrow 9} \frac{x^2 - 81}{x - 9}$$

is that correct..?

anonymous · Answer

$$\lim_{x \rightarrow 9} \frac{ x ^{2}-81 }{ x-9 }$$

solomonzelman · Answer

use:  $\large\color{black}{  a^2-b^2=(a-b)(a+b)     }$   for the top

campbell_st · Answer

so factor the numerator, its the difference of 2 squares.... 

then you'll see a common factor to remove. 

and finally substitute x = 9 into whats left to find the limit

anonymous · Answer

yes, well is the answer 18? 
I did (x+9)(x-9)/(x-9), simplified it to (x+9) and substituted 9 for x and added and got 18...

solomonzelman · Answer

yes.

solomonzelman · Answer

that is right:)

anonymous · Answer

Ok thanks so much:)) you rock:))

campbell_st · Answer

well done

solomonzelman · Answer

you welcome!