Q. 4 - Calculus

Question

Describe the punctured interval around $x=2$ that has a radius of $3$ and the punctured interval around $x=4$ that has a radius of $0.25$. 

Step-by-Step Solution

Answer

The punctured interval around $x=2$that has a radius of$3$ is $\left(-1,3\right)\cup \left(3,5\right)$.

The punctured interval around $x=4$that has a radius of $0.25$ is $\left(3.75,4\right)\cup \left(4,4.25\right)$.   

Step 1. Given information.

Describe the punctured interval around $x=2$ that has a radius of $3$ and the punctured interval around $x=4$ that has a radius of $0.25$. 

Step 2. Calculation.

The radius for $x=2 \mathrm{is} 3$.

The punctured interval will be:

$\left(2-3,3\right)\cup \left(3,3+2\right)=\left(-1,3\right)\cup \left(3,5\right)$.

Step 3. Calculation.

The radius for $x=4 \mathrm{is} 0.25$.

The punctured interval will be:

$\left(4-0.25,4\right)\cup \left(4,4+0.25\right)=\left(3.75,4\right)\cup \left(4,4.25\right)$