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

Question

let f(x)= 

 

sqrt(-2-x)+4 if x<-3

 

4 if x=-3

 

3x+14 if x> -3

 

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

 

lim(x->-3^-) f(x)= 

 

 

lim(x->-3^+)  f(x)=

 

lim(x->-3)  f(x)= 

Answer 1

to solve this equation

 

for the let f(x)= 
 
sqrt(-2-x)+4 if x<-3
 
4 if x=-3
 
3x+14 if x> -3

 

lim sqrt(-2-x)+4 (input -3 into the equation) = 5

x → -3 (on the left side approach -3.001)

 

lim 3x+14 (input -3 into the equation) = 5

x→ -3 (on the right side approach -2.999)

 

The left and right side both approaching toward 5, then the solution is limit for f(x) = 5

The actual solution at x = -3 is still  f(x) = 4.