Use the graph as shown to determine the following limits, and discuss the continuity of the function at .(i) (ii) (iii)
A)2 , 2 , 2 , not continuous
B)2 , 2 , 2 , continuous
C)3 , 3 , 3 , not continuous
D)3 , 3 , 3 , continuous
E)-3 , -3 , -3 , continuous

Question

Use the graph as shown to determine the following limits, and discuss the continuity of the function at  .(i)  (ii)  (iii)  
A)2 , 2 , 2 , not continuous 
B)2 , 2 , 2 , continuous 
C)3 , 3 , 3 , not continuous 
D)3 , 3 , 3 , continuous 
E)-3 , -3 , -3 , continuous

Quizplus · Accepted Answer

(i) The limit at 11ec1854_fdca_0f4f_acfc_59a3b2ef29e1_TBX8702_11 is 2 because as x approaches 2 from the left or the right, f(x) approaches 2. 
(ii) The limit at 11ec1854_fdca_0f50_acfc_0742c455652a_TBX8702_11 is 2 because as x approaches 3 from the left or the right, f(x) approaches 2. 
(iii) The limit at 11ec1854_fdca_0f51_acfc_29005b27ef90_TBX8702_11 is 2 because as x approaches 4 from the left or the right, f(x) approaches 2. 
Therefore, the limits at all three points are 2. 
However, the function is not continuous at 11ec1854_fdca_0f4e_acfc_07032c63fff8_TBX8702_11 because the limit as x approaches 3 does not equal the value of the function at that point (the function is undefined at x=3).

Use the Graph as Shown to Determine the Following Limits