BuyFind*launch*

4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 1.3, Problem 57E

(a)

To determine

**To sketch:** The graph of the Heaviside function.

Expert Solution

The Heaviside function is,

Use online graphing calculator and draw the graph of the Heaviside function as shown below in Figure1.

From Figure1, it is observed the Heaviside function is a piece-wise continuous function.

(b)

To determine

**To sketch:** The graph of

Expert Solution

The formula for

Observe that when

Thus, the formula for

Use online graphing calculator and draw the graph of

From Figure2, it is observed that the voltage is 0 when *t* = 0.

(c)

To determine

**To sketch:** The graph of the voltage in a circuit if the switch is turned on at t = 5 seconds and 240 volts are applied to the circuit; write the formula for

Expert Solution

Given that the time is *t* = 5 seconds.

Express the time as,

Thus, the formula for

Use online graph calculator and draw the graph of the voltage

From Figure 3, notice that the number 5 is not included in the domain as the switch is turned on at *t* = 5 seconds.