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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 (-5[1])approximately n over (15[1])this function of n. (15[2])The alternating harmonic series (15[1])converges to this function of 2. This function of n (*) factorial can be approximated using Stirling’s (10[1])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

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Buzzes

PlayerTeamOpponentBuzzpointValue
Skanda VasishtaBig Brown BallersAlbanian Rift in the Sky32-5
Skand ParvatikarLeif Eriksen's Striking Appearancewhatever3515
Taman TruongBasileus II: Electric BoogalooAlways Set the Kurve3915
Xander DiGiovanniPrat PackWith Less Than 2 Years of Combined Quizbowl Experience3915
Andrew NucciDon't Ever Take Sides Against the FamilyMidnight Bus to Vista4315
Annika LarsonAlbanian Rift in the SkyBig Brown Ballers5910

Summary

TournamentEditionMatchHeardConv. %Power %Neg %Avg. Buzz
VAULT II at Georgia Tech2026-01-24✕683%67%33%38.00
Triangle Cup2026-03-13✓3100%0%67%108.00
VAULT II at Eden Prairie HS2026-03-13✓3100%33%33%75.33
VAULT II at McGill2026-03-13✓4100%0%25%91.25
VAULT II at UCSB2026-03-13✓5100%80%20%43.00
VAULT II Northern UK2026-04-24✓3100%67%33%57.00
VAULT II Southern UK2026-04-24✓4100%50%25%66.00
VAULT II at Harvard2026-04-30✓3100%33%33%68.33
VAULT II at MINT2026-06-19✓580%20%40%85.25
VAULT II Stanford Online2026-07-17✓8100%50%50%58.13