Find the horizontal asymptotes. etf (t) =1+e-

ft=et1+e-t Now as t→∞, ft→∞. & limt →-∞ft=limt →-∞et1+e-t=limt →-∞et0-e-t By using…

Answered: et f (t) = 1+e-

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.4: Hyperbolas

Problem 5ECP: Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.

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Question

Find the horizontal asymptotes.

Expert Solution

Given,

$f (t) = \frac{e^{t}}{1 + e^{- t}}$

Now as $t \to \infty$ , $f (t) \to \infty$ .

$\begin{array}{rcl} \lim_{t \to - \infty} f (t) & = & \lim_{t \to - \infty} \frac{e^{t}}{1 + e^{- t}} \\ = & \lim_{t \to - \infty} (\frac{e^{t}}{0 - e^{- t}}) [B y u \sin g L' H o s p i t a l' s r u l e] \\ = & \lim_{t \to - \infty} (\frac{e^{t}}{- e^{- t}}) \\ = & - \lim_{t \to - \infty} (e^{2 t}) \\ = & 0 \end{array}$

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