Round 7: Tossup 14
This function of a complex number, z, is defined as this function of its modulus plus i times theta. The number of primes less than or equal to a real number n is approximately n over this function of n. The alternating harmonic series converges to this function of 2. This function of n (*) factorial can be approximated using Stirling’s approximation. The first three terms of the Taylor series of this function of 1 plus x is x minus x squared over 2 plus x cubed over 3. This function’s derivative is 1 over x. For 10 points, name this function whose inverse is e to the x. ■END■
ANSWER: natural logarithm [or natural log or ln; prompt on logarithm]
<Science - Math, Vikram Narasimhan> | VAULT II Packet 07
= Average correct buzzpoint
Buzzes
| Player | Team | Opponent | Buzzpoint | Value |
|---|---|---|---|---|
| Max Green | East Chapel Hill | Chapel Hill A | 18 | -5 |
| Matthew Medina | Grimsley | Cary Academy | 71 | -5 |
| Arjun Pant | Cary Academy | Grimsley | 108 | 10 |
| Robert Wisdom | Chapel Hill A | East Chapel Hill | 108 | 10 |
| Sowrish Komaragiri | Tantaene Animis Caelestibus Irae | Chapel Hill B | 108 | 10 |
Summary
| Tournament | Edition | Match | Heard | Conv. % | Power % | Neg % | Avg. Buzz |
|---|---|---|---|---|---|---|---|
| VAULT II at Georgia Tech | 2026-01-24 | ✕ | 6 | 83% | 67% | 33% | 38.00 |
| Triangle Cup | 2026-03-13 | ✓ | 3 | 100% | 0% | 67% | 108.00 |
| VAULT II at Eden Prairie HS | 2026-03-13 | ✓ | 3 | 100% | 33% | 33% | 75.33 |
| VAULT II at McGill | 2026-03-13 | ✓ | 4 | 100% | 0% | 25% | 91.25 |
| VAULT II at UCSB | 2026-03-13 | ✓ | 5 | 100% | 80% | 20% | 43.00 |
| VAULT II Northern UK | 2026-04-24 | ✓ | 3 | 100% | 67% | 33% | 57.00 |
| VAULT II Southern UK | 2026-04-24 | ✓ | 4 | 100% | 50% | 25% | 66.00 |
| VAULT II at Harvard | 2026-04-30 | ✓ | 3 | 100% | 33% | 33% | 68.33 |
| VAULT II at MINT | 2026-06-19 | ✓ | 5 | 80% | 20% | 40% | 85.25 |
| VAULT II Stanford Online | 2026-07-17 | ✓ | 8 | 100% | 50% | 50% | 58.13 |