Concepto de Límite.

Understanding the Concept of Limits in Functions

Introduction to Limits

• The limit of a function f(x) as x approaches a value b is defined as the value that the dependent variable y will take as x gets closer to b .

Graphical Representation of Limits

• A graphical analysis using the function f(x) = x + 2 illustrates how values approach a specific point. For example, as x nears 8, we can observe corresponding values for y .

Approaching Values on the Graph

• As we evaluate different values approaching 8 (e.g., when x = 7, 6, 4, etc.), we see that:

• When x = 2, then y = 4.

• When approaching from lower values like x = 7, it trends towards a limit of approximately 10.

Calculating Limits Algebraically

• The mathematical expression for this limit can be represented as:

• Limit of function:

• lim_x to 8 (x + 2)

• This notation captures both the function and its behavior as it approaches a specific value.

Solving for Limits

• To find the limit algebraically, substitute the approaching value into the function:

• Thus, substituting gives us:

• Limit when x to 8:

• Resulting in an output of 10 for this particular case.