for the function use algebra to find each of the following limits

Question

For the function
f(x)= {x^2−4, 0≤x<3
f(x)= {−1, x=3

f(x)= {3x-4, 3 less than x

 

use algebra to find each of the following limits:

 

lim f(x)=

x→3^+

lim f(x)=

x→3^-

lim f(x)=

x→3 

(For each, enter DNE if the limit does not exist.)

Answer 1

lim_x→3⁺  f(x) = lim_x→3⁺ (3x-4) = 5

 

lim_x→3^-  f(x) = lim_x→3^-  (x²-4) = 5

 

Since the one-sided limits are equal, lim_x→3 f(x) = 5