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b 1 f (x) dx b a a Let m and M be the minimum and maximum values of f on [a, b] (The existence of m and M is guaranteed by Theorem 14.2.) Thus, m f (x) M for all x in [a, b], so that Problem 30.3(c) gives

Fig. 2-45 By Ohm s law iL Now an application of KVL gives RS Vb VZ iZ iL 1 vL V 8:2 0:911 A Z 9 RL RL

and we use (1) to size RS for maximum Zener current IZ at the largest value of Vb : RS 1:1 12 8:2 2:62 1 0:911

Now we check to see if iZ ! 75 mA at the lowest value of Vb : iZ Vb vZ 0:9 12 8:2 0:911 81:3 mA iL 2:62 RS

1. The market value of a xed asset at the end of its service is known as a ______. 2. The uniform distribution of depreciation over the life of the asset is known as the _______ method. 3. The ______ method is used to write off the asset based on a series of fractions. 4. The method that produces the largest amount of depreciation in the earlier years, then rapidly declines, is known as the _______ method. 5. When income produced by an asset is the same each year, the rec ommended method of depreciation is ______. 6. When use rather than time is the key factor, _______ is the pre ferred method of depreciation. Answers: 1. scrap value; 2. SL; 3. SYD; 4. DDB; 5. SL; 6. UOP

m(b a)

A Zener diode has the speci cations VZ 5:2 V and PD max 260 mW. Assume RZ 0. (a) Find the maximum allowable current iZ when the Zener diode is acting as a regulator. (b) If a single-loop circuit consists of an ideal 15-V dc source VS , a variable resistor R, and the described Zener diode, nd the range of values of R for which the Zener diode remains in constant reverse breakdown with no danger of failure.

a (b) By KVL, VS RiZ VZ so that R Vs VZ iZ iZ max IZ PD max 260 10 3 50 mA VZ 5:2

f (x) dx M(b a)

From Section 2.10, we know that regulation is preserved if R VS VZ 15 5:2 1:96 k 0:1IZ max 0:1 50 10 3 VS VZ 15 5:2 196 IZ max 50 10 3

A light-emitting diode (LED) has a greater forward voltage drop than does a common signal diode. A typical LED can be modeled as a constant forward voltage drop vD 1:6 V. Its luminous intensity Iv varies directly with forward current and is described by Iv 40iD % millicandela (mcd) A series circuit consists of such an LED, a current-limiting resistor R, and a 5-V dc source VS . Find the value of R such that the luminous intensity is 1 mcd.

But then, by the intermediate-value theorem (Theorem 17.4), the value V is assumed by f somewhere in [a, b].

By (1), we must have iD From KVL, we have VS RiD 1:6 V 1:6 5 1:6 136 R S iD 25 10 3 Iv 1 25 mA 40 40

Early in this chapter, a new subsidiary ledger, called Accounts Receiv able, was created for all a company s customers. A rm that purchases on account would do the same thing, because the credit balance in Accounts Payable represents the total amount owed by the company for purchases on account.

The reverse breakdown voltage VR of the LED of Problem 2.32 is guaranteed by the manufacturer to be no lower than 3 V. Knowing that the 5-V dc source may be inadvertently applied so as to reverse-bias the LED, we wish to add a Zener diode to ensure that reverse breakdown of the LED can never occur. A Zener diode is available with VZ 4:2 V, IZ 30 mA, and a forward drop of 0.6 V. Describe the proper connection of the Zener in the circuit to protect the LED, and nd the value of the luminous intensity that will result if R is unchanged from Problem 2.32.

Write Then, g(x) g(x + h) g(x) = = =