Question

evaluate and explain how
lim x approaches -4+ (abs(x+4)/(x+4))(x+2)

Answer 1

\[\lim_{x\to -4^+}\] means \(x\) is approaching \(-4\) from numbers greater than \(-4\)
if \(x>-4\) then \(|x+4|=x+4\)

Answer 2

and also lim x approaches -4- (abs(x+4)/(x+4))(x+2)

Answer 3

so you are looking at
\[\frac{x+4}{(x+4)(x+2)}=\frac{1}{x+2}\]

Answer 4

and then
\[\lim_{x\to -4^+}\frac{1}{x+2}=\frac{1}{-4+2}=-\frac{1}{2}\]

Answer 5

no the (x+2) is multiplied by the whole thing

Answer 6

ok, that is not really the point anyway

Answer 7

\[ |x+4| = \left\{\begin{array}{rcc}
-x-4 & \text{if} & x <-4 \\
x+4& \text{if} & x \geq -4
\end{array}
\right.
\]

Answer 8

ohh i understand now the absolute value is broken down to have 2 values

Answer 9

and so
\[\frac{|x+4|}{x+4}= \left\{\begin{array}{rcc}
-1 & \text{if} & x <-4 \\
1& \text{if} & x> -4
\end{array}
\right.\]

Answer 10

right, and when you divide by \(x+4\) you will either have \(1\) or \(-1\) depending on whether \(x>-4\) or \(x<-4\)

Answer 11

ohh i understand makes sense thanks!!!!!

Answer 12

yw