Calculate the following limits

Question

Let f(x) = √(-3-x)+1, if x<-4

let f (x)= 1, if x=-4

let f (x)= 3x+14, if x>-4

 

Calculate the following limits. Enter DNE for a limit which does not exist 

lim x->-4^-

f(x)=

 

lim x->-4⁺

f(x)=

 

lim x->-4 

f(x)=

Answer 1

1) To find the lim_x->-4^- we will use the first equation because that function is defined for all values smaller than -4. 

 

Thus, lim_x->-4- √(-3-x)+1=√(-3-(-4))+1=2

 

Therfore we see that the  lim_x->-4^- f(x)=2

 

2) To find the lim_x->-4⁺ we will consider the third equation because that function is defined for all values bigger than -4.

 

Thus, lim_x->-4⁺ 3x+14=3(-4)+14

 

Therefore we see that the  lim_x->-4⁺ f(x) =2

 

3) To find the lim_x->4, we will use the fact that if the lim_x->-4^- = 2 and if lim_x->4⁺ = 2, then lim_x->-4 =2.