Question

When $t$ approaches infinity, limit of $\frac{1}{t} - \frac{t}{t²}$

A) $0$
B) $-[infinity]$
C) $1$
D) $[infinity]$

Answer 1

The limit of the function \( \frac{1}{t} - \frac{t}{t^2} \) as t approaches infinity is 0, because both terms \( \frac{1}{t} \) and \( -\frac{1}{t} \) approach 0. Thus, the correct answer is A) 0.

Step-by-step explanation:

The question asks about the limit of the function \( \frac{1}{t} - \frac{t}{t^2} \) as t approaches infinity. To determine this limit, you need to evaluate the behavior of each term separately as t approaches infinity.

The first term \( \frac{1}{t} \) approaches 0 because the numerator remains constant while the denominator grows without bound. For the second term, \( -\frac{t}{t^2} \), you can simplify the expression to -\( \frac{1}{t} \), which also approaches 0 as t approaches infinity for the same reason the first term does.

So, by adding the limits of the two terms, we find that the limit of the whole function as t approaches infinity is 0, making the correct answer A) 0.