The graph of f(x) = sin(2x)/x is shown in Figure 20. Is the function f(x) continuous at x = 0? Why or why not?

Expert Solution

Definition of Continuity:

A function f (x) is continuous at x = a provided all three of the following conditions hold true:

• Condition 1: f (a) exists.

• Condition 2: limx→af(x) exists at x = a .

• Condition 3: limx→af(x) = f(a)

If a function f (x) is not continuous at x = a, the function is discontinuous at x = a .

Consider the following graph drawn using Maple.

The function f(x) = sin(2x)/x is discontinuous at x = 0, since the function is not defined for x = 0. The condition 1 is violated. At x = 0, the graphing utility evaluates x→0f(x) = limx→0sin(2x)/x = 2.

Junaid answered 1 year ago

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