فارسی · Curriculum · Week 6 guide · Worked solutions
65 minutes · 100 points. Show your reasoning and include units in circuit answers.
- 20 points. Evaluate the limit of (x² − 36)/(x − 6) as x → 6. Give the domain restriction. If the value at 6 is assigned to be 20, explain the effect on the limit.
- 20 points. Evaluate the limit of (√(x + 16) − 4)/x as x → 0 using the conjugate. Explain why the denominator of the simplified expression allows substitution.
- 10 points. For |x + 3|/(x + 3) as x → −3, find both one-sided limits and decide whether a two-sided limit exists.
- 30 points. Node v connects to VA = 10 V through 4 kΩ, VB = −8 V through 8 kΩ, and ground through 8 kΩ. Find the two voltage contributions and the total. Check the three signed resistor currents, defined as leaving the node.
- 20 points. In Question 4 add a source injecting 1 mA into v. Find its contribution, the new node voltage, and the load power. Explain why summing partial load powers gives the wrong answer.