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Final

# MAT133Y1 Final: MAT133 FINAL FORMULA SHEET

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Department
Mathematics
Course
MAT133Y1
Professor
D Jill Tate
Semester
Fall

Description
MAT133 FINAL FORMULA SHEET Effective π β― Continuously π = ππ β― Rate πβ―= (1 + )πβ 1 Compounding π = ππ β―β―β― PV Annuities β― β―β― FV Annuities (1 + π) β 1 (t=0) 1 β (1 + π) (t=n) π = π β π r = effective π΄ = π β π period rate FV Annuity 1 + π β―β―β―β 1 PV Annuity 1 β 1 + π β―β―β― π = π β ( β 1) π΄ = π β ( + 1) Due π Due π Monthly π΄ Perpetuity π π = β―β― (No FV) π΄ = π Mortgage 1 β (1 + π) Payment π Effective β―β― 1 β (1 + π)β―β― π β― Bond Price π = π(1 + π) + ππ β Monthly π = (1 + 2 π Interest Rate β― Indefinite Definite Integrals π π₯ ππ₯ = πΉ π₯ + πΆ Integrals π π₯ ππ₯ = [πΉ π β πΉ π ] β―β― πππ₯ = ππ₯ + πΆ β―π π₯ Β± π π₯ ππ₯ β―β―β― β― π₯ ππ₯ = π₯ + πΆ = π π₯ ππ₯ π + 1 β―β― 1 ππ₯ = ln π₯ + πΆ More Common Β± β―π π₯ ππ₯ Common π₯ Integrals (including β― β― Integrals β― β― π π₯ ππ₯ = β π π₯ ππ₯ π ππ₯ = π + πΆ definite) β― β― β― β― β― π ππ₯ = π + πΆ π π₯ ππ₯ = π π₯ ππ₯ πππ β― β― β― ππ π₯ ππ₯ = π π π₯ ππ₯ + π π₯ ππ₯ β― β― Substitution π π π₯ π π₯ ππ₯ = π π’ ππ’ By Parts π’ππ£ = π’π£ β π£ππ’ π€βπππ π’ = π π₯ ,ππ’ = πβ²(π₯) Improper β― β― π π₯ ππ₯ = lim π π₯ ππ₯ Integrals β― β―ββ― β― Β±β β― Average 1 β― β πππ£ππππππ‘ π π₯ ππ₯ = lim π π₯ ππ₯ π = π π₯ ππ₯ ππππ π‘πππ‘ β―β― β―ββ―β― Value π β π β― β ππππ£ππππππ‘ β― β― β― π π₯ = π π₯ ππ₯ + π π₯ ππ₯ β―β― β―β― β― Consumer β―β― β―β― & Area β―β― Calculation π΄ = π¦1 β π¦2 ππ₯ + π¦2 β π¦1 + β― Producer πΆπ = π π β π0 ππ β―β―β― β―β― Surplus β―β―β― (y=β¦x) A = π₯1 β π₯2 ππ¦ + π₯2 β π₯1 ππ¦ + β― (p=β¦q) (x=β¦y) β―β― β―β― ππ = π0 β π π ππ (q0, p0) = β― equilibrium PV Continuous β― FV Continuous β― Annuity π π‘ πβ―β―β―ππ‘ π π‘ πβ―(β―β―β―)ππ‘ T = years β― Annuity β― ππ§ π π₯ + β,π¦ β π(π₯,π¦) ππ§ π π₯,π¦ + β β π(π₯,π¦) = π π₯,π¦ = lim = πβ―π₯,π¦ = lim ππ₯ β― β―ββ― β ππ¦ β―ββ― β Competitive Products Complementary Products β―β―β― β―β―β― β―β―β― β―β―β― > 0 πππ > 0 < 0 πππ < 0 β―β―β― β―β―β― β―β―β― β―β―β― Chain Rule Critical Point πππ‘ π§ = π π₯,π¦ ,π₯ = π₯ π,π  ,π¦ = π,π  π π₯,π¦ = 0 β― ππ§ = ππ§ Γ ππ₯ + ππ§ Γ ππ¦
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