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- 15 points. The domain excludes 5 (5 points). Factoring gives x + 5 on the original domain (5). Both sides approach 10 (5).
- 15 points. The left and right limits are −2 and 3 (6). The point value is 7 (4). The two-sided limit fails because the side limits differ (5).
- 20 points. The domain is [−2, ∞) (5). For x = −1.99 and −1.9999, the outputs are 0.1 and 0.01 (5). The positive gap x + 2 shrinks to zero, giving a right-hand limit of 0 (5). No real domain inputs lie to the left (5).
- 20 points. (v − 14)/4 + (v − 4)/8 + v/8 = 0 in mA (8). Multiplying by 8 gives 4v − 32 = 0, so v = 8 V (5). The outgoing currents are −1.5, 0.5 and 1 mA (7).
- 15 points. Set the outgoing sum to −2 mA, giving 4v − 32 = −16 and v = 4 V (5). The currents are −2.5, 0 and 0.5 mA (5). Their sum is −2 mA. Both ends of the branch to 4 V are at 4 V, so its current is zero (5).
- 15 points. (v − 12)/4 + v/8 = 1 (5). Thus 3v = 32 and v = 32/3 V (5). The outgoing currents are −1/3 and 4/3 mA, which sum to 1 mA (5).