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:

$\begin{gathered} \lim _{x\to0}\frac{|x|}{4x} \\ \Rightarrow\frac{x}{4x}=\frac{1}{4} \\ \Rightarrow\lim _{x\to0}\frac{1}{4} \\ \lim _{x\to0}\frac{1}{4}=\frac{1}{4} \\ =\frac{1}{4} \\ \\ \lim _{x\to-0.03}\frac{|x|}{4x} \\ \Rightarrow\frac{x}{4x}=\frac{1}{4} \\ \Rightarrow\lim _{x\to-0.03}\frac{1}{4}=\frac{1}{4} \\ =\frac{1}{4} \\ \\ \lim _{x\to-0.02}\frac{|x|}{4x} \\ \Rightarrow\frac{x}{4x}=\frac{1}{4} \\ \Rightarrow\lim _{x\to-0.02}\frac{1}{4}=\frac{1}{4} \\ =\frac{1}{4} \end{gathered}$

We proceed, we have:

$\begin{gathered} \lim _{x\to-0.01}\frac{|x|}{4x} \\ \Rightarrow\frac{x}{4x}=\frac{1}{4} \\ \Rightarrow\lim _{x\to-0.03}\frac{1}{4}=\frac{1}{4} \\ =\frac{1}{4} \\ \\ \lim _{x\to0.01}\frac{|x|}{4x} \\ \Rightarrow\frac{x}{4x}=\frac{1}{4} \\ \Rightarrow\lim _{x\to0.01}\frac{1}{4}=\frac{1}{4} \\ =\frac{1}{4} \\ \\ \lim _{x\to0.02}\frac{|x|}{4x} \\ \Rightarrow\frac{x}{4x}=\frac{1}{4} \\ \Rightarrow\lim _{x\to0.02}\frac{1}{4}=\frac{1}{4} \\ =\frac{1}{4} \end{gathered}$

Therefore, for the limit is 1/4