Question

Let f(x)= { [4x+1-sin(pi/x), x<2]  [cube root 3sqrt(3^x -1), x ≥ 2] }

a) Find lim x approaching 2 from the left f(x) and lim x approacvhes 2 from the right f(x).

b) Find lim x approaching 2 f(x) or explain why it does not exist

Answer 1

Step 1:

a) The piece wise function

 

Find limit of ,as approaches 2 from the left side.

.

Step 2:

Find limit of , as approaches 2 from the right side.

.

Step 3:

b) and .

Since the left hand side limit is not equal to the right hand side limit, limit doesn't exists.

The limit of doesn't exists as approaches to 2.

Solution:

a) and .

b) The limit of doesn't exists as approaches to 2.