Preview Activity 5.1.1.
Complete each of the following statements with an appropriate number or the symbols \(\infty\) or \(-\infty\text{.}\) Do your best to do so without using a graphing utility; instead use your understanding of the function’s graph.
(a)
(b)
(c)
(d)
As \(t \to 0^+\text{,}\) \(e^{-t} \to \). (When we write \(t \to 0^+\text{,}\) this means that we are letting \(t\) get closer and closer to \(0\text{,}\) but only allowing \(t\) to take on positive values.)
(e)
(f)
As \(t \to \frac{\pi}{2}^-\text{,}\) \(\tan(t) \to \). (When we write \(t \to \frac{\pi}{2}^-\text{,}\) this means that we are letting \(t\) get closer and closer to \(\frac{\pi}{2}^-\text{,}\) but only allowing \(t\) to take on values that lie to the left of \(\frac{\pi}{2}\text{.}\))
(g)
As \(t \to \frac{\pi}{2}^+\text{,}\) \(\tan(t) \to \). (When we write \(t \to \frac{\pi}{2}^+\text{,}\) this means that we are letting \(t\) get closer and closer to \(\frac{\pi}{2}^+\text{,}\) but only allowing \(t\) to take on values that lie to the right of \(\frac{\pi}{2}\text{.}\))
