Q. 3 - Calculus

Question

What are punctured intervals, and why do we need to use them when discussing limits?

Step-by-Step Solution

Answer

The punctured interval is defined on $(c-\delta , c) \cup (c, c+\delta )$where $\delta >0$represents a small distance to the left and right of $x=c$.

Step 1. Given information.

What are punctured intervals, and why do we need to use them when discussing limits?

Step 2. Statement.

The punctured interval is defined on $(c-\delta , c) \cup (c, c+\delta )$, where $\delta >0$ represents a small distance to the left and right of $x=c$.

The limits are never be concerned with what happens at the point $x=c$, only near the point $x=c$.

If we are calculation the value at$x=3$ for the function $f\left(x\right)=4x$, then we can use both $f(2.99) \mathrm{and} f(3.01)$ within any small unit of $f\left(3\right)=4\left(3\right)=12$.