Q. 28 - Calculus

Question

Use algebra to find the largest possible value of δ or smallest possible value of N that makes each implication true. Then verify and support your answers with labeled graphs.
$\text{ If }x>N\text{, then }1-2x<-500$

Step-by-Step Solution

Answer

We get $N=250.5$

Step1. Given information.

We have been given:

$\text{ If }x>N\text{, then }1-2x<-500$

We have to use algebra to find the largest possible value of δ or smallest possible value of N that makes each implication true.

Step 2. Find the value of N.

We have $1-2x<-500$.

So we can write:

$$\begin{gathered} 1-2x<-500 \\ -2x<-500-1 \\ -2x<-501 \\ 2x>501 \\ x>\frac{501}{2} \\ x>250.5 \end{gathered}$$

Since $x>N$,

$N=250.5$