Day 16 - Unit 6 Review | Eastern Kentucky University

University:
Eastern Kentucky University
Course:
MAT 234 | Calculus I
Academic year:

2025
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0

Pages:

3
Author:

Kira Hatcher

AP Calculus AB Name:_____________________________ Unit 6 Review Date: _______________ Slope Fields **Match slope fields to differential equations or functions** 𝑑𝑦 1. The slope field for the differential equation 𝑑𝑥 = 𝑥 + 𝑦 is shown. a. Sketch the solution curve through (0,1). b. Sketch the solution curve through (-3,0) Indefinite Integrals Write the general solution for the integrals below: 2. ∫ 2𝑥(15𝑥 4 − 2𝑥 2 − 3) 𝑑𝑥 2 sin 𝑥 4. ∫ cos2 𝑥 𝑑𝑥 36𝑥 2 6. ∫ (4𝑥 3+5)5 𝑑𝑥 3. ∫(24𝑥 5 + 3 20 √𝑥 2 3 9 + 𝑥 4 )𝑑𝑥 4 sin 𝑥 5. ∫ 3 tan 𝑥 𝑑𝑥 7. ∫ 12𝑥 2 √𝑥 3 − 5 𝑑𝑥 Pd: _______ 8. ∫ 2𝑥 2 +7𝑥−3 𝑥−2 1 𝑑𝑥 10. ∫5 (3𝑥 − 4)10 𝑑𝑥 9. ∫ 𝑥 3 −6𝑥−20 𝑥+5 𝑑𝑥 3 11.∫−1(−𝑥 3 + 3𝑥 2 − 1)𝑑𝑥 12. Find the particular solution for 𝑓 ′ (𝑠) = 10𝑠 − 12𝑠 3 where 𝑓(3) = 2. 13. Find the particular solution given 𝑓"(𝑥) = 2, 𝑓′(4) = 1, 𝑓(−1) = 2. Separable Differentiation Write the general solution for the differential equations below. 14. 16. 𝑑𝑦 𝑑𝑥 𝑑𝑦 𝑑𝑥 𝑥3 = 𝑦2 15. 𝑑𝑦 = 3𝑒 𝑥−𝑦 17. 𝑑𝑦 𝑑𝑥 𝑑𝑥 1 = sec2 𝑦 = 2𝑥𝑒 2𝑦 Write the particular solution for the differential equations below. 18. 𝑑𝑦 𝑑𝑥 3𝑥 2 = 𝑒 2𝑦 , 𝑦(1) = 0 19. 𝑑𝑦 𝑑𝑥 = 1+𝑥 2 𝑦2 3 , 𝑦(−1) = −√4 Write the equation of the tangent lines below. 20. 𝑓(𝑥) = −𝑥 3 + 3𝑥 2 + 3 𝑎𝑡 𝑥 = −1 21. 𝑓(𝑥) = 𝑥2 3𝑥+3 𝑎𝑡 𝑥 = −2

Day 16 - Unit 6 Review