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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 1.3, Problem 58E

(a)

To determine

**To sketch:** The graph of the ramp function

Expert Solution

Heaviside function is,

So, the ramp function is,

Use online graph calculator and draw the graph of the ramp function as shown below in Figure 1.

From Figure1, it is noted that the graph is a ray with starting point 0.

(b)

To determine

**To sketch:** The graph of circuit if the switch is turned at t = 0 and the voltage gradually increased to 120 volts in 60 seconds; write the formula for

Expert Solution

The formula for

**Given:**

The voltage

**Calculation:**

Let the ramp function be

Find the value of *c.*

Since

It is known that

Therefore, equation(1) becomes,

Thus, the ramp function is

Therefore,

Use online graph calculator and draw the graph of

From Figure1, it is noted that the graph is a ray with starting point 0.

(c)

To determine

**To sketch:** The graph of the voltage in a circuit if the switch is turned at *t* = 7 seconds and gradually increased t0 100 volts over a period of 25 seconds; write the formula for

Expert Solution

The formula for

The voltage varies from 0 to 100 in 25 seconds.

Therefore,

Therefore, the ramp function becomes,

The switch is turned at *t* = 7 seconds

That is, the time

Therefore, the formula for

Thus,

The function,

Use online graph calculator and draw the graph of

From Figure 3, it is noted that the voltage reaches to 100 in 25 seconds.