What is the limit of (2x + 3) as x approaches 2?

What is the limit of (2x + 3) as x approaches 2?

• A. 5
• B. 6
• C. 7
• D. 8

Answer: (C)

To determine the limit of the expression \( (2x + 3) \) as \( x \) approaches 2, you can substitute 2 directly into the expression since it is a polynomial function, which is continuous everywhere. Starting with the function: \[ 2x + 3 \] Substituting \( x = 2 \): \[ 2(2) + 3 = 4 + 3 = 7 \] Thus, as \( x \) approaches 2, the value of \( 2x + 3 \) approaches 7. Therefore, the limit of \( (2x + 3) \) as \( x \) approaches 2 is indeed 7, confirming that this is the correct answer. Understanding this concept of continuity is crucial because it allows us to simplify the process of finding limits for polynomial functions with direct substitution.

To determine the limit of the expression ( (2x + 3) ) as ( x ) approaches 2, you can substitute 2 directly into the expression since it is a polynomial function, which is continuous everywhere.

Starting with the function:

[

2x + 3

]

Substituting ( x = 2 ):

[

2(2) + 3 = 4 + 3 = 7

]

Thus, as ( x ) approaches 2, the value of ( 2x + 3 ) approaches 7. Therefore, the limit of ( (2x + 3) ) as ( x ) approaches 2 is indeed 7, confirming that this is the correct answer.

Understanding this concept of continuity is crucial because it allows us to simplify the process of finding limits for polynomial functions with direct substitution.