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Prove that $\lim_{h\to 0}\,\frac{0}{h}=0.$

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Lesson Parent:

Problem:

Answer:

It is true that $\lim_{h\to 0}\,\frac{0}{h}=0.$

Solution:

Recall that in general when

For this particular problem, we need to show that for every <Sign in to see all the formulas> there exists a <Sign in to see all the formulas> such that if <Sign in to see all the formulas> then <Sign in to see all the formulas>. The important thing to note is that $0/h=0$ except when $h=0$ . When $h=0$ then $0/h$ is undefined since we cannot divide by zero. However, our function limit proof states that we evaluate the function $0/h$ for values of $h$ in <Sign in to see all the formulas>. In particular, <Sign in to see all the formulas> means that we evaluate the function $0/h$ at values of <Sign in to see all the formulas>.