فارسی · Curriculum · Week 5 guide · Solutions
70 minutes · Closed notes · Calculator permitted · 100 points. Show branch reasoning, current directions and units. Allow 30 minutes afterward for correction.
- 15 points. For (x² − 25)/(x − 5), state its original domain and find the limit at 5 with an algebraic explanation.
- 15 points. A piecewise model gives −2 for x < 0, 3 for x > 0 and 7 at 0. Give both one-sided limits, the point value and the conclusion about the two-sided limit.
- 20 points. For the real rule √(x + 2), give the domain, the right-hand limit at −2, and a reason the left-hand approach is unavailable. Use two sample inputs and justify the trend from the rule.
- 20 points. Node v is connected to 14 V through 4 kΩ, to 4 V through 8 kΩ, and to ground through 8 kΩ. With no injection, write KCL, solve for v and give the three signed outgoing currents.
- 15 points. Add a 2 mA sink to the circuit in Question 4. Find the new voltage and currents. Check their signed sum and explain the direction of current in the 4 V branch.
- 15 points. A different node connects to 12 V through 4 kΩ and to ground through 8 kΩ. A source injects 1 mA. Find v and verify KCL with the two signed outgoing currents.