Question

In: Math

For the following exercises, refer to Figure 15. Each square represents one square unit....x = 4

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 = 4

Expert Solution

A function f (x) is continuous at x = 4 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 textbook:

From the graph, it is clear that:

f(a) = f(4)

Since f(4) exists, condition 1 is satisfied.

From the graph, it is clear that:

limx→4-f(x) = 2

limx→4+f(x) = 2

Since limx→4-f(x) = limx→4+f(x)

So, limx→4f(x) exists, condition 2 is satisfied.

From the graph, it is clear that:

f(4) = -3

limx→4f(x) = 2

Since limx→4f(x) = ≠ f(4), condition 3 is not satisfied.

Junaid answered 1 year ago

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Question

For the following exercises, refer to Figure 15. Each square represents one square unit....x = 4

Solutions

Expert Solution

Related Solutions

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