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36.9 Find the indicated limits: 5x 3 4x + 3 (a) lim x + 2x 2 1 1 1 (d) lim sin x x 0 x x3 x2 + x 1 (g) lim x 1 x + ln x 1 (j) (m) (p)

Example 8.9. For the BJT ampli er circuit of Fig. 3-10, assume CC ! 1. The small-signal equivalent circuit is given by Fig. 8-4 where RB R1 kR2 . Let hoe hre 0, hfe 90, R1 1 k , R2 16 k , RE 500 , CE 330 F, RC 1 k , and RL 10 k . Use SPICE methods to determine the low-frequency cuto point.

CHAP. 8]

ln(1 + ex ) x + 1 + x 1 ex (e) lim x x 0 1 1 (h) lim ln(x + 1) x x 0 3x 2x (k) lim x x 0 (b) lim (n) (q)

The netlist code that follows describes the circuit:

Ex8_9.CIR vi 1 0 AC 0.250V R1 1 0 1kohm R2 1 0 16kohm Vsen 1 2 DC 0V Rhie 2 3 200ohm Fhfe 3 4 Vsen 90 RE 3 0 500ohm CE 3 0 330uF RC 4 0 1kohm RL 4 0 10kohm .AC DEC 25 10Hz 10kHz .PROBE .END

(c) (f ) (i) (l) (o) (r) (u)

Solved Problem 11.1 Equipment of $400 is sold to a retailer at a 25 per cent trade discount. What is the retailer s cost Solution: Trade Discount: $400 times 25% = $100 List Price $400 Trade Discount 100 Net Cost $300 Solved Problem 11.2 If transportation of $20 were added to the purchase in Solved Problem 11.1, what would be the net cost Solution: Net cost: $300 + 20 (Transportation costs) = $320 Transportation costs are added to the net cost of the item and are not sub ject to trade discounts. Solved Problem 11.3 Julie Pearman bought $800 of supplies for her company, less chain discounts of 30 percent and 20 percent. (a) What is the single equivalent discount (b) What is the net cost to the company Solution: (a) (100% 30%) times (100% 20%) = 70% times 80% = 56% Single equivalent discount = 44% (100% 56%) (b) $800 times 44% = $352 Net cost = $448 ($800 $352) Solved Problem 11.4 Determine the last day allowable for a company to take advantage of the full discount. Term (a) 2/10, n/30 (b) 2/10, 1/15, n/30 Date of Order June 4 June 4 Delivery Date June 8 June 8

Execute hEx8_9.CIRi and use the Probe feature of PSpice to yield the plots of Fig. 8-13. From the marked points, it is seen that the low-frequency cuto is fL 214:4 Hz, where the voltage gain has a value of AvL 289:7:

Fig. 8-13

1 cos x x x 0 x2 lim x + (ln x)3 tan x lim x 0 x ex lim 2 x 0 x x3 1 lim x 1 x + 1 sin x lim x x 0+ e3x 1 lim x 0 tan x lim

The above example utilized the small-signal equivalent circuit. Small-signal analysis frequency sensitivity can also be implemented using the SPICE model of the transistor directly.

Example 8.10. For the BJT ampli er of Fig. 3-10, let Ri RE 0, RC 3 k , R1 1 k , R2 15 k , CC1 CC2 1 F, and VCC 15 V. The transistor can be modeled by the parameters of Example 3.4, except Rb 10 , Rc 100 , and Cje 100 pF. Use SPICE methods to graphically show the voltage gain magnitude and phase angle over the frequency range of 100 Hz to 1 GHz and to determine the low- and high-frequency cuto points where fL depends on the value of the bypass capacitor CE and fH depends on the BJT junction capacitance values.