Question

Number 2 investigate the following limits using graph and table, Record at least 5 values of the function on either side of a. Tell what the limit is, if it doesn’t exist explain why ? Use the x values -0.03, -0.02, -0.01, 0, 0.01, 0.02

Answer 1

We were given:

`\begin{gathered} \lim _(x\to0)(|x|)/(4x) \\ \Rightarrow(x)/(4x)=(1)/(4) \\ \Rightarrow\lim _(x\to0)(1)/(4) \\ \lim _(x\to0)(1)/(4)=(1)/(4) \\ =(1)/(4) \\ \\ \lim _(x\to-0.03)(|x|)/(4x) \\ \Rightarrow(x)/(4x)=(1)/(4) \\ \Rightarrow\lim _(x\to-0.03)(1)/(4)=(1)/(4) \\ =(1)/(4) \\ \\ \lim _(x\to-0.02)(|x|)/(4x) \\ \Rightarrow(x)/(4x)=(1)/(4) \\ \Rightarrow\lim _(x\to-0.02)(1)/(4)=(1)/(4) \\ =(1)/(4) \end{gathered}`

We proceed, we have:

`\begin{gathered} \lim _(x\to-0.01)(|x|)/(4x) \\ \Rightarrow(x)/(4x)=(1)/(4) \\ \Rightarrow\lim _(x\to-0.03)(1)/(4)=(1)/(4) \\ =(1)/(4) \\ \\ \lim _(x\to0.01)(|x|)/(4x) \\ \Rightarrow(x)/(4x)=(1)/(4) \\ \Rightarrow\lim _(x\to0.01)(1)/(4)=(1)/(4) \\ =(1)/(4) \\ \\ \lim _(x\to0.02)(|x|)/(4x) \\ \Rightarrow(x)/(4x)=(1)/(4) \\ \Rightarrow\lim _(x\to0.02)(1)/(4)=(1)/(4) \\ =(1)/(4) \end{gathered}`

Therefore, for the limit is 1/4