Question

If a is an arbitrary nonzero constant, what happens to a/b as b approaches 0

Answer 1

As b approaches 0, the expression a/b approaches infinity or negative infinity depending on the signs of a and b. This occurs because dividing a nonzero number by a number that gets closer and closer to 0 results in a value that increases without limit.

Step-by-step explanation:

When considering the expression a/b, where a is a nonzero constant and b approaches 0, we deal with a concept referred to in calculus as a limit.

As b approaches 0, the value of a/b becomes increasingly large in magnitude. If b approaches 0 from the positive side, a/b approaches positive infinity if a is positive, and negative infinity if a is negative. Conversely, if b approaches 0 from the negative side, a/b approaches negative infinity if a is positive, and positive infinity if a is negative. This behavior can be described by saying that a/b has an asymptote as b approaches 0. The reason for this is that you are dividing a nonzero number by an increasingly small number, which results in a value that grows without bound.

Answer 2

a/b tends to an infinite value

Step-by-step explanation:

If If a is an arbitrary nonzero constant, and we are to look for a/b as b approaches zero, we can represent this statement using limits. The statement is expressed as:

`\lim_(b \to 0) (a)/(b)`

Substituting b = 0 into the function

`= (a)/(0) \\\\= \infty \\\\\lim_(b \to 0) (a)/(b) = \infty\\ \\\\`

Since the limits of a tends to infinity as b tends to zero hence we can conclude that If a is an arbitrary nonzero constant then a/b tends to infinity or is undefined as b approaches 0