Problem 50 - Calculus of a Single Variable

Question

Finding a Limit What is the limit of \(g(x)=x\) as \(x\) approaches \(\pi ?\)

Step-by-Step Solution

Answer

The limit of \(g(x)=x\) as \(x\) approaches \(\pi\) is \(\pi\).

Step 1: Understand the nature of the function

The function given, \(g(x) = x\), is a linear function. The graph of such a function is a straight line, which means there are no jumps, breaks, or holes in the graph.

Step 2: Use the property of linear functions

The limit of a linear function as x approaches a particular value is the value of the function at that point. Therefore, to find \(\lim_{x \to \pi} g(x)\), we just need to find the value of g at \(\pi\).

Step 3: Substitute \(\pi\) into the function

Substitute \(\pi\) into the function \(g(x) = x\), so \(g(\pi) = \pi\).