Question

Number 9 Find the limit Use the x values: -0.03, -0.02, -0.01, 0, 0.01, 0.02, 0.03

Answer 1

In order to find the limit for the given question, we have to study the behavior of the function in the proximity of the point we want, which in the case of question 9 is x = 0. We will calculate the value of the function for x = -0.03, x = -0.02, x= -0.01, x= 0, x= 0.01, x = 0.02 and x=0.03. This will give us a good idea of the behavior.

`\begin{gathered} f(-0.03)=9-2\cdot(-0.03)=9.06 \\ f(-0.02)=9-2\cdot(-0.02)=9.04 \\ f(-0.01)=9-2\cdot(-0.01)=9.02 \\ f(0)=9-2\cdot0=9 \\ f(0.01)=9-2\cdot(0.01)=8.98 \\ f(0.02)=9-2\cdot(0.02)=8.96 \\ f(0.03)=9-2\cdot(0.03)=8.94 \end{gathered}`

We can see that when we approach x = 0 from both sides, the output of the function tends to 9. Therefore the limit is equal to 9.