Question

Use the given graph to determine the limit, if it exists. Find limit as x approaches two from the left of f of x. and limit as x approaches two from the right of f of x..

Answer 1

ANSWER

The limit does not exist.

EXPLANATION

From the graph the left hand limit is the value the graph is approaching as x-values approaches 2.

$\lim_{x \to {2}^{ - } }(f(x)) = 5$

Also the right hand limit is the value that the graph approaches, as x-values approach 2 from the right.

$\lim_{x \to {2}^{ + } }(f(x)) = - 3$

Since the left hand limit is not equal to the right hand limit, the limit as x approaches 2 does not exist

Answer 2

By the confront theorem we know that the limit only exists if both lateral limits are equal

In this case they aren't so we don't have limit for x approaching 2, but we can find their laterals.

Approaching 2 by the left we have it on the 5 line so this limit is 5

Approaching 2 by the right we have it on the -3 line so this limit is -3

Think: it's approaching x = 2 BUT IT'S NOT 2, and we only have a different value for x = 2 which is 1, but when it's approach by the left we have the values in the 5 line and by the right in the -3 line.