5 Steps to a 5 AP Calculus BC 2019
342 STEP 4. Review the Knowledge You Need to Score High Therefore,P= 200 ( 1 99 ) e.^369 t 1 + ( 1 99 ) e.^369 t = 200 e.^369 t ...
More Applications of Definite Integrals 343 13.12 Solutions to Cumulative Review Problems 3 ey=x^2 y 3 ey dy dx = 2 xy+ dy dx ...
344 STEP 4. Review the Knowledge You Need to Score High Step 4. Verify result by differentiating y=2(2x+1)^1 /^2 dy dx = 2 ( 1 2 ...
More Applications of Definite Integrals 345 s ̄(0)= ( −sin 0− 1 2 (0) ) ̄ı + (√ 3 2 (0)+cos 0 ) j ̄+C= 0 0 ̄ı+ 1 j ̄+C= 0 C=−j ̄ ...
CHAPTER 14 Big Idea 4: Series Series IN THIS CHAPTER Summary:In this chapter, you will learn different types of series and the m ...
Series 347 14.1 Sequences and Series Main Concepts:Sequences and Series, Convergence A sequence is a function whose domain is th ...
348 STEP 4. Review the Knowledge You Need to Score High Example 1 Determine whether the series ∑∞ n= 1 1 5 n converges or diverg ...
Series 349 Example 1 Determine whether the series 1+ 3 2 + 9 4 + 27 8 +···converges. 1+ 3 2 + 9 4 + 27 8 +···is a geometric seri ...
350 STEP 4. Review the Knowledge You Need to Score High 14.3 Convergence Tests Main Concepts:Divergence Test, Integral Test, Rat ...
Series 351 Example 3 Determine whether the series 1+ 1 2 + 1 3 + 1 4 +···+ 1 n +···= ∑∞ n= 1 1 n converges or diverges. Step 1: ...
352 STEP 4. Review the Knowledge You Need to Score High Step 2: nlim→∞ an+ 1 an =nlim→∞ ( (n+1)^3 (ln 2)n+^1 · (ln 2)n n^3 ) = 1 ...
Series 353 Informal Principle Given a rational expression containing a polynomial innas a factor in the numerator or denominator ...
354 STEP 4. Review the Knowledge You Need to Score High 14.4 Alternating Series Main Concepts:Alternating Series, Error Bound, A ...
Series 355 |S−s 3 |=| 3. 2 − 3. 25 |=|− 0. 05 |= 0 .05, which is clearly less thana 4 = 1 16 = 0 .0625. The coefficient ofa 4 is ...
356 STEP 4. Review the Knowledge You Need to Score High Step 1: Consider the series ∑∞ n= 1 ∣∣ ∣ ∣ (−1)n 3 n−^1 ∣∣ ∣ ∣=^1 + 1 3 ...
Series 357 The series ∑∞ n= 1 (−1)n 2 k+ 1 5 k− 1 =− 3 4 + 5 9 − 1 2 .... Note that limn→∞an=nlim→∞ 2 n+ 1 5 n− 1 =nlim→∞ 2 n+ 1 ...
358 STEP 4. Review the Knowledge You Need to Score High 14.6 Taylor Series Main Concepts:Taylor Series and MacLaurin Series, Com ...
Series 359 Step 3: f(0) 0! x^0 + f′(0) 1! x^1 + f′′(0) 2! x^2 + f′′′(0) 3! x^3 + f(4)(0) 4! x^4 = 0 1 x^0 + 1 1 x^1 + − 1 2 x^2 ...
360 STEP 4. Review the Knowledge You Need to Score High Example 1 Find the MacLaurin series forf(x)= 1 1 +x^2 . Step 1: Begin wi ...
Series 361 Step 2: Differentiate: − 1 (x+1)^2 =− 1 + 2 x− 3 x^2 + 4 x^3 −···= ∑∞ n= 0 (−1)n+^1 (n+1)xn. Step 3: Multiply by−1. 1 ...
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