Packet 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 (15[1])a real number (-5[1])n is approximately (15[2])n over this function (15[1])of n. The alternating harmonic series converge to this function of 2. This function of n (*) factorial can be approximated using Stirling’s approximation. (10[1]-5[1])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■ (0[1])

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
Sreyas SabbaniInnovation BChattahoochee B2715
Evan XueJohns CreekHoover30-5
Sean HarbisonExhibitionMidtown3315
Kaiden LeeNorthview ALambert B3315
Allan YuanHooverJohns Creek3715
Aarnav PatwardhanChattahoochee ANorthview B60-5
Viren KohliLambert AInnovation A6010
Reyansh KroviNorthview BChattahoochee A1080

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