Please show all steps clearly. Th **Question 7: Evaluating the Area Under a Function**Examine the given figure to determine the area under the function $ f(t) $.### Graph Description:- **Axes:** - **Horizontal Axis (t):** Represents time. - **Vertical Axis (f(t)):** Represents the function's value.- **Function Representation:** - This graph displays a triangular function symmetrical about the vertical axis ($ t = 0 $). - The base of the triangle spans from $ t = -\epsilon $ to $ t = \epsilon $. - The height of the triangle is $ \frac{1}{\epsilon} $.### Problems to Solve:**(a)** What is the duration of the function when $ \epsilon = 0 $?**(b)** What is the magnitude of $ f(0) $ when $ \epsilon = 0 $?

Answered: Find the area under the function shown…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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Please show all steps clearly. Th

Expert Solution

Step 1: (a) Duration of the function when ϵ = 0

The triangular pulse extends from $- ϵ$ to $+ ϵ$ . Therefore, the duration (or width) of the function is $2 ϵ$ .

When $ϵ = 0$ , the function essentially collapses to a singular point at $t = 0$ .

Thus, the duration of the function when $ϵ = 0$ is $0$ (i.e., it doesn't have any duration; it's just a point).

Detailed Explanation

The duration of the triangular function, as depicted, is from $- ϵ$ to $+ ϵ$ . This is a total duration of $2 ϵ$ .

However, as $ϵ$ approaches 0, the width of this triangle narrows, effectively squeezing the triangular function into an increasingly thin shape. If we were to let $ϵ$ actually become 0, the duration of the function would become 0 as well, meaning the triangle would be squeezed into a single point in time.

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