5 Steps to a 5 AP Calculus BC 2019
62 STEP 4. Review the Knowledge You Need to Score High To find the vertical asymptotes, look forx-values such that the denominat ...
Limits and Continuity 63 you notice that limx→ 0 +f(x)=∞, and limx→ 0 −f(x)=−∞. Therefore, the linex=0 (or they-axis) is a verti ...
64 STEP 4. Review the Knowledge You Need to Score High 5.3 Continuity of a Function Main Concepts:Continuity of a Function at a ...
Limits and Continuity 65 Example 2 Determine the intervals on which the given function is continuous: f(x)= ⎧ ⎨ ⎩ x^2 + 3 x− 10 ...
66 STEP 4. Review the Knowledge You Need to Score High [–3,8] by [–4,8] Figure 5.3-3 Example 5 Ifg(x)=x^2 − 2 x−15, using the In ...
Limits and Continuity 67 5.4 Rapid Review Findf(2) and limx→ 2 f(x) and determine iffis continuous atx=2. (See Figure 5.4-1.) ...
68 STEP 4. Review the Knowledge You Need to Score High Evaluate limx→ 5 − x^2 x^2 − 25 . Answer: The limit is−∞, since (x^2 −2 ...
Limits and Continuity 69 5.5 Practice Problems Part A The use of a calculator is not allowed. Find the limits of the following: ...
70 STEP 4. Review the Knowledge You Need to Score High Givenf(x) as shown in Figure 5.5-2, find (a) f(3). (b) xlim→ 3 +f(x). (c ...
Limits and Continuity 71 Rewrite limx→b x^3 −b^3 x^6 −b^6 as limx→b x^3 −b^3 (x^3 −b^3 )(x^3 +b^3 ) =limx→b 1 x^3 +b^3 . Subst ...
72 STEP 4. Review the Knowledge You Need to Score High Ast→ 3 +,(t−3)>0, and thus (t− 3 )= √ (t− 3 )^2. Rewrite the limit a ...
Limits and Continuity 73 (See Figure 5.7-3.) Ifb=0, thenr=0, butrcannot be 0. Ifb=−3,−2, or− 1 f would have more than one root. ...
AP-Calculus-BC 2727-MA-Book May 11, 2018 14:10 74 STEP 4. Review the Knowledge You Need to Score High To find horizontal asympt ...
CHAPTER 6 Big Idea 2: Derivatives Differentiation IN THIS CHAPTER Summary:The derivative of a function is often used to find rat ...
76 STEP 4. Review the Knowledge You Need to Score High 6.1 Derivatives of Algebraic Functions Main Concepts:Definition of the De ...
Differentiation 77 x f(x) x = a a f is discontinuous at x = a 0 y Figure 6.1-2 f has a corner at x = a y x f(x) (a, (f(a)) (^0) ...
78 STEP 4. Review the Knowledge You Need to Score High Example 2 Evaluate limh→ 0 cos(π+h)−cos(π) h . The expression limh→ 0 cos ...
Differentiation 79 TIP • Always write out all formulas in your solutions. Power Rule Iff(x)=cwherecis a constant, then f′(x)=0. ...
80 STEP 4. Review the Knowledge You Need to Score High Example 4 Using a calculator, findf′(x) and f′(3) if f(x)= 1 √ x . There ...
Differentiation 81 Example 4 Using your calculator, find an equation of the tangent to the curve f(x)=x^2 − 3 x+2at x=5. Find th ...
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