Question

Use the given graph to determine the limit, if it exists.

A coordinate graph is shown with an upward sloped line crossing the y axis at the origin that ends at the open point 3, 1, a closed point at 3, 7, and a horizontal line starting at the open point 3, 3.

Find limit as x approaches three from the right of f of x.

Answer 1

limit of f(x) as x approaches 3 from the right side.

x= 3.1 results in 3

x= 3.01 results in 3

x= 3.001 results in 3

limit as x approaches 3 from the right side is 3.

Answer 2

The limit as x approaches three from the right of f of x is:

3

Explanation:

Based on the graph we observe that the graph of the function increases continuously from x= -∞ to x=3.

There is a open circle at (3,1)

Then at x=3 it takes the value as 7

i.e. when x=3 then f(3)=7

Now after x=3 i.e. to the right of x=3 the graph is a constant line i.e. f(x)=3 for x>3

There is a open circle at (3,3)

Hence, the right hand limit of f(x) at x=3 is:

`\lim_(x \to 3^+) f(x)=3`