New: apostol-calculusAll contenthive-129948krhive-196917steemzzanhive-166405hive-185836hive-180932hive-183959hive-150122uncommonlabhive-144064photographylifehive-101145hive-183397bitcoinhive-188619hive-145157hive-184714krsuccesshive-193637hive-124908hive-109690hive-181136TrendingNewHotLikersshinday (30)in mathematics • 4 years ago[Apostol's Calculus] Exercises 1.5: Solution to 25Let S be the set of all vectors v such that v = < x , y, z > with 3x + 4y = 1 and z = 0. Then, x = and y = So, v = Proof: Assume S is a real linear space, then S must be…shinday (30)in mathematics • 4 years ago[Apostol's Calculus] Exercises 1.5: Solution to 23Let S be the set of all vectors v = in V3 with either x = 0 or y = 0. Assume S is a real linear space. Then, S must be closed under addition (axiom 1). Let v1 = ∈ S and let v2 = ∈ S…shinday (30)in hive-124500 • 4 years agoCompilation of Solutions to Tom Apostol's Infamously Rigourous Calculus Textbook (vol. 2)Hello! Someone else has already compiled solutions to all exercises in Tom Apostol's "Calculus", but on for vol. 1. As I am taking multivariable calculus this semester, I've decided it would be…shinday (30)in mathematics • 4 years ago[Apostol's Calculus] Exercises 1.5: Solution to 14Let S be the set of all functions f such that Assume that S is a real linear space. Then, by the addition axioms of real linear spaces, there must exist an element g in S such that f + g = 0. We…shinday (30)in apostol-calculus • 4 years ago[Apostol's Calculus] Exercises 1.5Notice: These proofs are my own. I am not a professional mathematician. If you notice errors or inconsistencies in these solutions, let me know! I appreciate all feedback. The key to solving these…
