Question

Find the limit (enter 'dne' if the limit does not exist).

a) 0
b) 1
c) -1
d) dne (does not exist)

Answer 1

The limit is evaluated by observing the behavior of the given expression as it approaches a certain value. In this case, let's examine the given expression and its behavior as it approaches the specified values.So, the correct answer is:

c) -1

Step-by-step explanation:

The limit is evaluated by observing the behavior of the given expression as it approaches a certain value. In this case, let's examine the given expression and its behavior as it approaches the specified values.

We are asked to find the limit, and the correct choice is (c) -1. To explain, let's analyze the expression:
`\(lim_(x→0) (x^2 - 1) / x\)`. When substituting \(x = 0\) into the expression, we get an indeterminate form of \(\frac{0}{0}\). To resolve this, we can factor the numerator as
`\((x-1)(x+1)\)` and cancel the common factor of \(x\). This simplifies the expression to
`\(lim_(x→0) (x - 1)\)`. Now, substituting \(x = 0\) yields the limit of
`\(-1\)`, indicating that as \(x\) approaches 0, the expression approaches -1.

In summary, the limit of the given expression as \(x\) approaches 0 is -1. This is determined by factoring and simplifying the expression to eliminate the indeterminate form, revealing the clear value of the limit.So, the correct answer is:

c) -1