5 Steps to a 5 AP Calculus AB 2019 - William Ma

MA 3972-MA-Book May 7, 2018 9:52 102 STEP 4. Review the Knowledge You Need to Score High 6.4 Rapid Review Findf(2) and limx→ 2 ...

MA 3972-MA-Book May 7, 2018 9:52 Limits and Continuity 103 Find the vertical and horizontal asymptotes off(x)= 1 x^2 − 25 . An ...

MA 3972-MA-Book May 7, 2018 9:52 104 STEP 4. Review the Knowledge You Need to Score High Givenf(x) as shown in Figure 6.5-2, fi ...

MA 3972-MA-Book May 7, 2018 9:52 Limits and Continuity 105 6.7 Solutions to Practice Problems Part A The use of a calculator is ...

MA 3972-MA-Book May 7, 2018 9:52 106 STEP 4. Review the Knowledge You Need to Score High Thus, you have 3 4 3 limx→ 0 sin 3x 3 x ...

MA 3972-MA-Book May 7, 2018 9:52 Limits and Continuity 107 The graph indicates that (a)f(3)=4, (b) limx→ 3 +f(x)=0, (c) limx→ 3 ...

MA 3972-MA-Book May 7, 2018 9:52 108 STEP 4. Review the Knowledge You Need to Score High Substitutingx=0 into | 3 x− 4 | x− 2 , ...

MA 3972-MA-Book May 9, 2018 10:9 CHAPTER 7 Big Idea 2: Derivatives Differentiation IN THIS CHAPTER Summary:The derivative of a f ...

MA 3972-MA-Book May 9, 2018 10:9 110 STEP 4. Review the Knowledge You Need to Score High 7.1 Derivatives of Algebraic Functions ...

MA 3972-MA-Book May 9, 2018 10:9 Differentiation 111 x f(x) x = a a f is discontinuous at x = a 0 y Figure 7.1-2 f has a corner ...

MA 3972-MA-Book May 9, 2018 10:9 112 STEP 4. Review the Knowledge You Need to Score High Example 2 Evaluate limh→ 0 cos(π+h)−cos ...

MA 3972-MA-Book May 9, 2018 10:9 Differentiation 113 TIP • Always write out all formulas in your solutions. Power Rule Iff(x)=cw ...

MA 3972-MA-Book May 9, 2018 10:9 114 STEP 4. Review the Knowledge You Need to Score High Example 4 Using a calculator, findf′(x) ...

MA 3972-MA-Book May 9, 2018 10:9 Differentiation 115 Example 4 Using your calculator, find an equation of the tangent to the cur ...

MA 3972-MA-Book May 9, 2018 10:9 116 STEP 4. Review the Knowledge You Need to Score High Example 3 Ify= ( 2 x− 1 x^2 ) 3 , find ...

MA 3972-MA-Book May 9, 2018 10:9 Differentiation 117 Example 2 Findf′(x)iff(x)=cot(4x−6). Using the chain rule, letu= 4 x−6. The ...

MA 3972-MA-Book May 9, 2018 10:9 118 STEP 4. Review the Knowledge You Need to Score High Example 8 Ify= tanx 1 +tanx , find dy d ...

MA 3972-MA-Book May 9, 2018 10:9 Differentiation 119 Example 2 Findf′(x)iff(x)=tan−^1 √ x. Letu= √ x.Then f′(x)= 1 1 +( √ x)^2 d ...

MA 3972-MA-Book May 9, 2018 10:9 120 STEP 4. Review the Knowledge You Need to Score High Example 1 y=e^3 x+ 5 xe^3 +e^3 dy dx =( ...

MA 3972-MA-Book May 9, 2018 10:9 Differentiation 121 Example 8 y=ln(lnx) Letu=lnx. Then dy dx = 1 lnx du dx = 1 lnx ( 1 x ) = 1 ...