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Example1

Title: Calculus

Grade Lesson s6-p1

Explanation: The best way to understand SAT-4 is by looking at some examples. Take turns and read each example for easy understanding.

Examples

Topics → Definition Example1 Example2

Determine if the function f(x) = 3x - 2 is continuous at x = 4.

Step: 1

To determine continuity, we need to check three conditions:

Explanation:

Here, let’s introduce and discuss three conditions.

Step: 2

Let’s evaluate each condition:

1. The function f(x) = 3x - 2 is defined for all real numbers, including x = 4. Therefore, the function is defined at x = 4.

Explanation:

Here, use the first condition to satisfy the given function.

Step: 3

2. To find the limit as x approaches 4, we substitute x = 4 into the function: \$ \lim_{x \to 4} 3x - 2 = 3(4) - 2 = 12 - 2 = 10 \$.

Thus, the limit of f(x) as x approaches 4 is 10.

Explanation:

Here, use the second condition to satisfy the function.

Step: 4

3. Now, we compare the value of the function at x = 4 with the limit: f(4) = 3(4) - 2 = 12 - 2 = 10.

The value of the function f(x) at x = 4 is equal to the limit.

Since all three conditions are satisfied, we can conclude that the function f(x) = 3x - 2 is continuous at x = 4.

Explanation:

Here, satisfying the third condition, we conclude that f(x) = 3x - 2 is continuous at x = 4.