Question

In: Math

For the following exercises, refer to Figure 15. Each square represents one square unit....x = 2

For the following exercises, refer to Figure 15. Each square represents one square unit. For each value of a, determine which of the three conditions of continuity are satisfied at x = a and which are not.

x = 2

Expert Solution

A function f (x) is continuous at x = a, only if it satisfies all the three following conditions:

• Condition 1: f (a) exists.

• Condition 2: limx→af(x) exists

• Condition 3: limx→af(x) = f(a)

Consider the graph provided in the exercise:

From the graph, it is clear that:

f(a) = f(2)

Since f(2) does not exist, condition 1 is not satisfied.

From the graph, it is clear that:

limx→2-f(x) = -1

limx→2+f(x) = -1

Since limx→2-f(x) = limx→2+f(x)

So, limx→2f(x) exists, condition 2 is satisfied.

Since, f(2) does not exist

So, limx→2f(x) ≠ f(2), condition 3 is not satisfied.

Junaid answered 1 year ago

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