5 Steps to a 5 AP Calculus BC 2019
322 STEP 4. Review the Knowledge You Need to Score High Example 2 Find a solution of the differentiation equation dy dx =xsin(x^ ...
More Applications of Definite Integrals 323 Step 6. Separate variables:dy=(x^2 +x−1)dx. Step 7. Integrate both sides: ∫ dy= ∫ (x ...
324 STEP 4. Review the Knowledge You Need to Score High Example 5 Write an equation for the curve that passes through the point ...
More Applications of Definite Integrals 325 (e.g., (2,−1), (2, 0), (2, 3), etc. ), dy dx =1. Also, remember that dy dx represent ...
326 STEP 4. Review the Knowledge You Need to Score High Example 3 A slope field for a differential equation is shown in Figure 1 ...
More Applications of Definite Integrals 327 (b) Sketch a possible graph for the particular solutiony=f(x) to the differential eq ...
328 STEP 4. Review the Knowledge You Need to Score High Step 5: Substitute initial condition (0, 3) and obtaink=3. Thus, you hav ...
More Applications of Definite Integrals 329 Exponentiation produces P K−P =e(kt+C^1 ) ⇒ P K−P =ekt·eC^1 ⇒ P K−P =C 2 ekt. Solvin ...
330 STEP 4. Review the Knowledge You Need to Score High Step 1: The rate of spread is dP dt =kP ( 1 − P 2000 ) . Step 2: The sol ...
More Applications of Definite Integrals 331 Example 2 Use Euler’s Method with a step size ofΔx= 0 .1 to computey(1) ify(x) is th ...
332 STEP 4. Review the Knowledge You Need to Score High tP. 3 P ( 1 − P 20 ) yn=yn− 1 +Δx· f′(xn− 1 ,yn− 1 ) 0 4 .96 4 +.5(.96)= ...
More Applications of Definite Integrals 333 Answer: Total number of gallons leaked= ∫ 10 0 5 e−^0.^1 tdt. How much money should ...
334 STEP 4. Review the Knowledge You Need to Score High Use Euler’s Method with a step size ofΔx= 0 .5 to computey(2), ify(x)is ...
More Applications of Definite Integrals 335 The change of temperature of a cup of coffee measured in degrees Fahrenheit in a ce ...
336 STEP 4. Review the Knowledge You Need to Score High Use Euler’s Method with a step size of Δx= 0 .5 to computey(3) ify(x)is ...
More Applications of Definite Integrals 337 13.11 Solutions to Practice Problems Part A The use of a calculator is not allowed. ...
338 STEP 4. Review the Knowledge You Need to Score High y(t)=y 0 ekt Half-life=4500 years⇒ 1 2 =e^4500 k. Take ln of both side ...
More Applications of Definite Integrals 339 Step 9. Verify result by differentiating: dy dx = x^2 2 − 5 x− 2 d^2 y dx^2 =x− 5. P ...
340 STEP 4. Review the Knowledge You Need to Score High eln ∣∣y 1 / 2 x+ 1 ∣∣ =eln 2 y^1 /^2 x+ 1 = 2 y^1 /^2 = 2 (x+ 1 ) y=( 2 ...
More Applications of Definite Integrals 341 Distance Traveled= ∫ 10 0 ∣∣ v(t) ∣∣ dt ∣∣ 2 − 6 e−t ∣∣ = { −( 2 − 6 e−t)if 0≤t< ...
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