Question

Find the limit of the function algebraically.

limit as x approaches negative two of quantity x squared minus four divided by quantity x plus two.

Answer 1

i)
`$\lim_{x\to\hspace{0.1cm}-2} ((x^(2) - 4))/(x + 2) $`
`= \hspace{0.1cm} $\lim_{x\to\hspace{0.1cm}-2} ((x-2)(x+2))/(x + 2) $`
`= \hspace{0.1cm} $\lim_{x\to\hspace{0.1cm}-2} (x-2) $` = -2 -2 = -4

Explanation:

i)
`$\lim_{x\to\hspace{0.1cm}-2} ((x^(2) - 4))/(x + 2) $`
`= \hspace{0.1cm} $\lim_{x\to\hspace{0.1cm}-2} ((x-2)(x+2))/(x + 2) $`
`= \hspace{0.1cm} $\lim_{x\to\hspace{0.1cm}-2} (x-2) $` = -2 -2 = -4