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AB与BC中常用的三角恒等式、求导法则与常见导数公式、积分基本公式与部分换元/反三角相关结果，并汇总极限与连续性、奇偶函数、周期性、介值定理、有理函数无穷处极限、渐近线、变化率、导数定义以及若干重要定理（如罗尔定理、平均值定理与极值定理）。适用于复习与快速查阅核心计算框架与常用结论。",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/template/","Template",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/template/presentations/","Presentations",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/template/final-notes-for-ab-and-bc-trigonometric-differentiation-integration-formulas-and-calculus-theorems/571648/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/final-notes-for-ab-and-bc-trigonometric-differentiation-integration-formulas-and-calculus-theorems/571648.png","ImageObject",442,249,{"name":42,"@type":43},"Muffet","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-22","2026-10-13",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",6,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What trigonometric identities are included in the notes?","Question",{"text":63,"@type":64},"The notes list key identities such as sin^2θ + cos^2θ = 1 and relationships involving tan, cot, sec, and csc, plus sum/difference formulas like sin(A+B), sin(A−B), and cos(A−B).","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"Which differentiation rules and derivative formulas are provided?",{"text":68,"@type":64},"They include product rule, quotient rule, chain rule, plus standard derivatives for trig functions (sin, cos, tan, cot, sec, csc) and exponential/logarithmic forms like e^x, a^x, ln x, and selected arc functions.",{"name":70,"@type":61,"acceptedAnswer":71},"What calculus theorems about limits and derivatives are summarized?",{"text":72,"@type":64},"The notes cover limits and continuity, even/odd behavior and periodicity, intermediate value theorem, rational-function limits at infinity, asymptotes, rate of change, the derivative definition, and the main theorems: Rolle’s theorem, mean value theorem, and extreme-value theorem.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},571648,1792360051,{"code":4,"msg":82,"data":83},"success",[84,88,93,98,103,108,113,118,123],{"id":85,"doc_module":22,"doc_module_name":25,"category_name":29,"show_sort_weight":86,"slug":87},11,90,"presentations",{"id":89,"doc_module":22,"doc_module_name":25,"category_name":90,"show_sort_weight":91,"slug":92},12,"Resumes",80,"resumes",{"id":94,"doc_module":22,"doc_module_name":25,"category_name":95,"show_sort_weight":96,"slug":97},14,"Invoices",70,"invoices",{"id":99,"doc_module":22,"doc_module_name":25,"category_name":100,"show_sort_weight":101,"slug":102},15,"Posters",60,"posters",{"id":104,"doc_module":22,"doc_module_name":25,"category_name":105,"show_sort_weight":106,"slug":107},16,"Social 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tan 2 θ = sec 2 θ  \n1 + cot 2 θ = csc 2 θ sin(−θ ) = − sinθ cos(−θ ) = cos θ tan(−θ ) = − tan θ  \nsin(A + B) = sin AcosB + sin B cos A  \nsin(A − B) = sin AcosB − sin B cos Acos(A + B) = cos A cos B − sin Asin B  \ncos(A − B) = cos A cos B + sin Asin B sin 2θ = 2 sinθcos θ  \n13. tan θ = scθθ = 1cot~~ ~~θ  \n14. cot θ = cossinθθ = ~~ ~~ta1n~~ ~~θ  \n15. sec θ = co1s~~ ~~θ  \n[16.](16. csc)[ csc](16. csc) θ = si1n~~ ~~θ  \n17. cos2 θ = ~~ ~~12 ( 1+ cos 2 θ )  \n18. sin 2 θ = ~~ ~~12 ( 1− cos 2 θ )  \ncos 2θ = cos2 θ − sin2 θ = 2 cos2 θ −1 = 1− 2 sin 2 θ  \nDifferentiation Formulas  \nddx~~ ~~ (x n ) = nx n−1  \nddx~~ ~~ ( fg) = fg ′ + gf ′ Product ruleddx~~ ~~ (~~ ~~fg~~ ~~) = gf~~ ~~′g−2~~ ~~fg~~ ~~′ Quotient ruleddx~~ ~~ f (g (x)) = f ′(g (x))g ′(x) Chain ruleddx~~ ~~ (sin x) = cos x  \nddx~~ ~~ (cos x) = − sin xddx~~ ~~ (tan x) = sec 2 xddx~~ ~~ (cot x) = − csc2 xddx~~ ~~ (sec x) = sec x tan xddx~~ ~~ (cscx) = − cscx cot x  \n11. ddx~~ ~~ (ex ) = ex  \n12. ddx~~ ~~ (a x ) = a x ln a  \n13. ddx~~ ~~ (ln x) = 1x  \n14. ddx~~ ~~ (Arc sin x) = 1~~ ~~x~~ ~~2~~ ~~  \n15. ddx~~ ~~ (Arc tan x) = 1~~ ~~+1x~~ ~~2~~ ~~  \n16. ddx~~ ~~ (Arc sec x) = |~~ ~~x~~ ~~|~~ ~~1x2~~ ~~−1  \n17. ddx~~ ~~ [ c ] = 0  \n18. ddx~~ ~~ cf ( x ) = cf ' ( x )  \nIntegration Formulas  \n1. ∫a dx = ax + C  \n2. ∫x n dx = xn11 + C, n ≠ −1  \n3. ∫ ~~ ~~1x~~ ~~ dx = ln x + C  \n4. ∫ ex dx = ex + C  \n5. ∫a x dx = lanxa + C  \n6. ∫ ln x dx = x ln x − x + C  \n7. ∫ sin x dx = − cos x + C  \n8. ∫ cos x dx = sin x + C  \n9. ∫ tan x dx = ln sec x + C or − lncos x + C  \n10. ∫ cot x dx = ln sin x + C  \n11. ∫ sec x dx = ln sec x + tan x + C  \n12. ∫ csc x dx = − ln csc x + cot x  + C  \n13. ∫ sec 2 x dx = tan x + C  \n14. ∫ sec x tan x dx = sec x + C  \n15. ∫ csc 2 x dx = − cot x + C  \n16. ∫ cscx cot x dx = − cscx + C  \n17. ∫ tan 2 x dx = tan x − x + C  \n18. ∫ ~~ ~~a~~ ~~2~~ ~~x~~ ~~2~~ ~~ = ~~ ~~1a~~ ~~ Arc tan􀂨􀂧􀂩 ~~ ~~xa~~ ~~ 􀂷􀂹􀂸 + C  \n19. ∫ ~~ ~~a~~ ~~d2~~ ~~x~~ ~~2~~ ~~ = Arc sin 􀂨􀂧􀂩 ~~ ~~xa~~ ~~ 􀂷􀂹􀂸 + C  \n20. ∫ ~~ ~~xxd2x−~~ ~~a~~ ~~2~~ ~~ = ~~ ~~1a~~ ~~ Arc sec ~~ ~~xa~~ ~~ + C = ~~ ~~1a~~ ~~ Arc cos ~~ ~~ax + C  \nFormulas and Theorems  \n1.  Limits and Continuity:  \nA function y = f (x) is continuous at x = a if  \ni) . f(a) exists  \nii) .  f ( x ) exists  \niii) .  f ( x ) = f (a) Otherwise, f is discontinuous at x = a.  \nThe limit a f ( x ) exists if and only if both corresponding one-sided limits exist and are equal – that is,  \na f ( x ) = L → a+ f ( x ) = L = a − f ( x )  \n2.  Even and Odd Functions  \n1. A function y = f (x) is even if f (−x) = f (x) for every x in the function’s domain. Every even function is symmetric about the y-axis.  \n2. A function y = f (x) is odd if f (−x) = − f (x) for every x in the function’s domain. Every odd function is symmetric about the origin.  \n3.  Periodicity  \nA function f (x) is periodic with period p (p > 0) if f (x + p) = f (x) for every value of x.  \nNote: The period of the function y = Asin(Bx + C) or y = Acos(Bx + C) is 2πB~~ ~~ . The amplitude is A . The period of y = tan x is π .  \n4.  Intermediate-Value Theorem  \nA function y = f (x) that is continuous on a closed interval [a, b] takes on every value between f (a) and f (b) .  \nNote: If f is continuous on [a, b] and f (a) and f (b) differ in sign, then the equation f (x) = 0 has at least one solution in the open interval (a, b) .  \n5.  Limits of Rational Functions as  x → ±∞  \ni) . xl ~~ ~~fg~~(~~(xx~~)~~) = 0 if the degree of f (x) \u003C the degree of g (x) Example: lim ~~ ~~x23−~~ ~~2x = 0  \nx→∞ x + 3  \nii) . lim f (x) is infinite if the degrees of f (x) > the degree of g (x)  \nx→±∞ g (x)  \nExample: lim ~~ ~~x32+~~ ~~2x = ∞  \nx→∞ x − 8  \niii) . lim f (x) is finite if the degree of f (x) = the degree of g (x)  \nx→±∞ g (x)  \nExam~~pl~~e:  ~~ ~~2x120x−−3x5x2 = − ~~ ~~25  \n6.  Horizontal and Vertical Asym","cbCaigwiMbCMVZnF","https://ap.wps.com/l/cbCaigwiMbCMVZnF","pdf",176864,"English","# Trigonometric Formulas\n# Differentiation Formulas\n# Integration Formulas\n# Formulas and Theorems\n## Limits and Continuity\n## Even and Odd Functions\n## Periodicity\n## Intermediate-Value Theorem\n## Limits of Rational Functions as x→±∞\n## Horizontal and Vertical Asymptotes\n## Average and Instantaneous Rate of Change\n## Definition of Derivative\n## The Number e as a Limit\n## Rolle’s Theorem\n## Mean Value Theorem\n## Extreme-Value Theorem","[{\"question\":\"What trigonometric identities are included in the notes?\",\"answer\":\"The notes list key identities such as sin^2θ + cos^2θ = 1 and relationships involving tan, cot, sec, and csc, plus sum/difference formulas like sin(A+B), sin(A−B), and cos(A−B).\"},{\"question\":\"Which differentiation rules and derivative formulas are provided?\",\"answer\":\"They include product rule, quotient rule, chain rule, plus standard derivatives for trig functions (sin, cos, tan, cot, sec, csc) and exponential/logarithmic forms like e^x, a^x, ln x, and selected arc functions.\"},{\"question\":\"What calculus theorems about limits and derivatives are summarized?\",\"answer\":\"The notes cover limits and continuity, even/odd behavior and periodicity, intermediate value theorem, rational-function limits at infinity, asymptotes, rate of change, the derivative definition, and the main theorems: Rolle’s theorem, mean value theorem, and extreme-value theorem.\"}]","Final Notes for AB and BC - Trigonometric, Differentiation, Integration Formulas and Calculus Theorems | PDF",1791922951]