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ap_calculus_ab [2024/04/10 07:50] – mrdoughap_calculus_ab [2024/05/12 23:54] (current) – [AP Calc AB Study Guide] 172.88.72.108
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 ====== AP Calc AB Study Guide ====== ====== AP Calc AB Study Guide ======
 +  * Credit: Simplestudies.org 
 +  * This study guide has a lot of images so if u cant scroll to the very bottom without jittering just let it load for a bit 
 +  * Here is a Cheat Sheet/Shorter and compressed version of what's described. [[https://drive.google.com/file/d/1oTnZ5zSmNq0RWiAuZzW8q0ki5WLdhy70/view?usp=sharing|Final Notes for AB and BC]] 
 +  * Limit evaluation chart: [[https://drive.google.com/file/d/1bhdygywT-doVSjAEXM8BYZGj5CiAtQEV/view?usp=sharing|here]] 
 +  * Key words pdf [[https://drive.google.com/file/d/1MXi1LwqLF00C2uRe8h-i3E1SBnJdSmrk/view?usp=sharing|here]]
 ====== Unit 1 – Limits and Continuity ====== ====== Unit 1 – Limits and Continuity ======
  
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 [[AP_Calc_AB_Study_Guide_f289051ba2044b4ab01d25945296aa61:Untitled_11|{{AP_Calc_AB_Study_Guide_f289051ba2044b4ab01d25945296aa61:Untitled_11.png}}]]that means f(x) equals h(x) and g(x) [[AP_Calc_AB_Study_Guide_f289051ba2044b4ab01d25945296aa61:Untitled_11|{{AP_Calc_AB_Study_Guide_f289051ba2044b4ab01d25945296aa61:Untitled_11.png}}]]that means f(x) equals h(x) and g(x)
  
-====== Unit 2 - Differentiation: Definition and Basic DerivativeRules ======+====== Unit 2 - Differentiation: Definition and Basic Derivative Rules ======
  
 **What is a derivative?** **What is a derivative?**
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   * The derivative of f(x) is denoted as f’(x) or   * The derivative of f(x) is denoted as f’(x) or
  
-[[AP_Calc_AB_Study_Guide_f289051ba2044b4ab01d25945296aa61:Untitled_12|{{AP_Calc_AB_Study_Guide_f289051ba2044b4ab01d25945296aa61:Untitled_12.png}}]]**Derivatives as Limits**+[[AP_Calc_AB_Study_Guide_f289051ba2044b4ab01d25945296aa61:Untitled_12|{{AP_Calc_AB_Study_Guide_f289051ba2044b4ab01d25945296aa61:Untitled_12.png}}]] 
 +**Derivatives as Limits**
  
-[[AP_Calc_AB_Study_Guide_f289051ba2044b4ab01d25945296aa61:Untitled_13|{{AP_Calc_AB_Study_Guide_f289051ba2044b4ab01d25945296aa61:Untitled_13.png}}]]**Steps to find derivatives as limits:**+[[AP_Calc_AB_Study_Guide_f289051ba2044b4ab01d25945296aa61:Untitled_13|{{AP_Calc_AB_Study_Guide_f289051ba2044b4ab01d25945296aa61:Untitled_13.png}}]] 
 +**Steps to find derivatives as limits:**
  
   - Identify the form of the derivative first (look at the image above)… is it form a? b? c?   - Identify the form of the derivative first (look at the image above)… is it form a? b? c?
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 [[AP_Calc_AB_Study_Guide_f289051ba2044b4ab01d25945296aa61:Untitled_14|{{AP_Calc_AB_Study_Guide_f289051ba2044b4ab01d25945296aa61:Untitled_14.png}}]][[AP_Calc_AB_Study_Guide_f289051ba2044b4ab01d25945296aa61:Untitled_15|{{AP_Calc_AB_Study_Guide_f289051ba2044b4ab01d25945296aa61:Untitled_15.png}}]][[AP_Calc_AB_Study_Guide_f289051ba2044b4ab01d25945296aa61:Untitled_16|{{AP_Calc_AB_Study_Guide_f289051ba2044b4ab01d25945296aa61:Untitled_16.png}}]]**Derivatives of Trigonometric Functions:** [[AP_Calc_AB_Study_Guide_f289051ba2044b4ab01d25945296aa61:Untitled_14|{{AP_Calc_AB_Study_Guide_f289051ba2044b4ab01d25945296aa61:Untitled_14.png}}]][[AP_Calc_AB_Study_Guide_f289051ba2044b4ab01d25945296aa61:Untitled_15|{{AP_Calc_AB_Study_Guide_f289051ba2044b4ab01d25945296aa61:Untitled_15.png}}]][[AP_Calc_AB_Study_Guide_f289051ba2044b4ab01d25945296aa61:Untitled_16|{{AP_Calc_AB_Study_Guide_f289051ba2044b4ab01d25945296aa61:Untitled_16.png}}]]**Derivatives of Trigonometric Functions:**
  
-[[AP_Calc_AB_Study_Guide_f289051ba2044b4ab01d25945296aa61:Untitled_17|{{AP_Calc_AB_Study_Guide_f289051ba2044b4ab01d25945296aa61:Untitled_17.png}}]]  * HINT: If the original function starts with C, then the derivative is negative!+[[AP_Calc_AB_Study_Guide_f289051ba2044b4ab01d25945296aa61:Untitled_17|{{AP_Calc_AB_Study_Guide_f289051ba2044b4ab01d25945296aa61:Untitled_17.png}}]]   
 +* HINT: If the original function starts with C, then the derivative is negative!
     * Example: cosx, cotx, & cscx     * Example: cosx, cotx, & cscx
  
 **Derivative Rule for LN** **Derivative Rule for LN**
  
-[[AP_Calc_AB_Study_Guide_f289051ba2044b4ab01d25945296aa61:Untitled_18|{{AP_Calc_AB_Study_Guide_f289051ba2044b4ab01d25945296aa61:Untitled_18.png}}]]  * HINT: [Derive over copy]+[[AP_Calc_AB_Study_Guide_f289051ba2044b4ab01d25945296aa61:Untitled_18|{{AP_Calc_AB_Study_Guide_f289051ba2044b4ab01d25945296aa61:Untitled_18.png}}]]   
 +* HINT: [Derive over copy]
     * Example: h(x) = ln(2x^2 + 1)     * Example: h(x) = ln(2x^2 + 1)
       * First derive 2x^2 + 1. That would be 4x! And then put that over theoriginal function, which would be 2x^2 + 1.       * First derive 2x^2 + 1. That would be 4x! And then put that over theoriginal function, which would be 2x^2 + 1.
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 **Deriving Exponential Functions** **Deriving Exponential Functions**
  
-[[AP_Calc_AB_Study_Guide_f289051ba2044b4ab01d25945296aa61:Untitled_19|{{AP_Calc_AB_Study_Guide_f289051ba2044b4ab01d25945296aa61:Untitled_19.png}}]]**Continuity**+[[AP_Calc_AB_Study_Guide_f289051ba2044b4ab01d25945296aa61:Untitled_19|{{AP_Calc_AB_Study_Guide_f289051ba2044b4ab01d25945296aa61:Untitled_19.png}}]] 
 + 
 +**Continuity**
  
 A function f is continuous at “c” if: A function f is continuous at “c” if:
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 Example: Example:
  
-[[AP_Calc_AB_Study_Guide_f289051ba2044b4ab01d25945296aa61:Untitled_20|{{AP_Calc_AB_Study_Guide_f289051ba2044b4ab01d25945296aa61:Untitled_20.png}}]][[AP_Calc_AB_Study_Guide_f289051ba2044b4ab01d25945296aa61:Untitled_21|{{AP_Calc_AB_Study_Guide_f289051ba2044b4ab01d25945296aa61:Untitled_21.png}}]]====== Unit 3 - Differentiation: Composite, Implicit, and InverseFunctions ======+[[AP_Calc_AB_Study_Guide_f289051ba2044b4ab01d25945296aa61:Untitled_20|{{AP_Calc_AB_Study_Guide_f289051ba2044b4ab01d25945296aa61:Untitled_20.png}}]][[AP_Calc_AB_Study_Guide_f289051ba2044b4ab01d25945296aa61:Untitled_21|{{AP_Calc_AB_Study_Guide_f289051ba2044b4ab01d25945296aa61:Untitled_21.png}}]] 
 +====== Unit 3 - Differentiation: Composite, Implicit, and InverseFunctions ======
  
 **The Chain Rule** **The Chain Rule**
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 [[AP_Calc_AB_Study_Guide_f289051ba2044b4ab01d25945296aa61:Untitled_29|{{AP_Calc_AB_Study_Guide_f289051ba2044b4ab01d25945296aa61:Untitled_29.png}}]][[AP_Calc_AB_Study_Guide_f289051ba2044b4ab01d25945296aa61:Untitled_30|{{AP_Calc_AB_Study_Guide_f289051ba2044b4ab01d25945296aa61:Untitled_30.png}}]]**Higher-Order Derivatives** [[AP_Calc_AB_Study_Guide_f289051ba2044b4ab01d25945296aa61:Untitled_29|{{AP_Calc_AB_Study_Guide_f289051ba2044b4ab01d25945296aa61:Untitled_29.png}}]][[AP_Calc_AB_Study_Guide_f289051ba2044b4ab01d25945296aa61:Untitled_30|{{AP_Calc_AB_Study_Guide_f289051ba2044b4ab01d25945296aa61:Untitled_30.png}}]]**Higher-Order Derivatives**
  
-[[AP_Calc_AB_Study_Guide_f289051ba2044b4ab01d25945296aa61:Untitled_31|{{AP_Calc_AB_Study_Guide_f289051ba2044b4ab01d25945296aa61:Untitled_31.png}}]]====== Unit 4 - Contextual Applications of Differentiation ======+[[AP_Calc_AB_Study_Guide_f289051ba2044b4ab01d25945296aa61:Untitled_31|{{AP_Calc_AB_Study_Guide_f289051ba2044b4ab01d25945296aa61:Untitled_31.png}}]] 
 +====== Unit 4 - Contextual Applications of Differentiation ======
  
 **Particle Motion** **Particle Motion**
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