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Welcome to AP Calculus AB!The purpose of this assignment is to have you practice the skills necessary to be successful in AP Calculus. All of the skills in this packet are skills that you have mastered prior to taking this course. Each question was carefully selected and every question is equally important. There should be NO calculators used in completing this assignment unless otherwise specified. AP Calculus AB is a fast paced course that is equivalent to a college level class, and there is a lot of material that must be covered before the AP exam in May. Due to this, we cannot use class time to reteach prerequisite skills.There will be a quiz in this week of school that will be based on this packet.To help with this assignment, you can reference Khan Academy, YouTube, etc. to assist you, but NOT to give you answers.Good luck!LawhonDiagnostics Test:You will complete a diagnostic test using the link below. Print or screen shot your results and send them to me at ReviewLinear EquationsWrite the linear equations for the given information in Standard Form, Slope Intercept Form, and Point Slope Form.1. Through -4, 1 and (2, -5)2. Through 2, -3 and (-3, 7)3. Through 2, 8 and parallel to y=56x-14. Through 1, 7 and parallel to y=3x+5 5. Through 4, 7 and perpendicular to y=-2x+96. Through 3, 2 and perpendicular to 2x-5y=3PolynomialsFactor the following completely:1. x2+12xy+20y22. x2+3xy-10y23. 2x2+11x+124. 5x2+9x-25. 16x2-256. 121x2-36y27. 16x2+56xy+49y28. 8x4+44x3+56x29. x3+110. 3x3-81Divide using a method of your choice:1. 6x4-3x3+5x2+2x-63x2-22. x3-x2-10x+10x-33. 2x4-3x2+7x+8x2+x-34. 4x3+2x2-4x+32x+3FunctionsUse the following functions for these problems:fx=3-5x-2x2gx=x2x+6hx=1-x21. f(4)2. f(0)3. f(-3)4. f(6-x)5. f(7-4x)6. f(x+h)7. g(0)8. g(-3)Compute f(gx) and g(fx) for the following functions:1. fx=4x-1, gx=6+7x2. fx=5x+2, gx=x2-14x3. fx=x2-2x+1, gx=8-3x24. fx=x2+3, gx=5+x2Compute f-1(x) of the following function:1. fx=6x+152. fx=3-29x3. fx=x3+64. fx=4x-35+21Find all vertical asymptotes for the function:1. fx=1x22. fx=x2x2-4Find all horizontal/slant asymptotes for the function:1. fx=x2-2x+1x3+x-72. fx=5x3-2x2+84x-3x3+5Perform the following operations:1. 1x+1+xx-6 - 5x-2x2-5x-62. 3x+5x+5-x-12-x- 4x2-3x-1x2+3x-10Solve the following equations:A calculator may be used for the final answer only. Round to the hundredths place.1. log3(x-2)=32. log4(17x-4)=33. log2x-log2x-1=24. log5(x-3)=log5x+35. 4+3x+1=86. 5ex=227. 103x-1=578. 2e3x-5=79. 151+e-2x+1=410. 101+3-x=2Trigonometry:Find the exact values of the following:1. sinπ22. cosπ63. tan3π44. sec7π65. sin5π66. csc2π3 7. sec-π38. tan(-2π3)9. csc3π210. secπ11. cotπ2 12. tan2πSimplify the following identities:1. sinx+sinxcot2x2. sinxcscx-cos2x3. 1-1sec2xsecxsin2x4. sinxtanxsinxxcsc2x + cos2xcsc2x5. sinx+tanx1+secx6. cotx+1sinx+cosxFind ALL solutions on the interval [0, 2π]:1. tan2x-3=02. 2cos2x-3cosx=03. sin2x-sinx=24. cos2x+cosx=sin2x5. 3tan3x-3tan2x-tanx+1=06. 2cos2x-3=0-62230-33591500AP Calculus Self-Teaching:The ability to teach yourself a mathematics topic is a skill that will be both necessary and invaluable throughout college and the rest of your life. It will also be necessary in AP Calculus as the amount of material and limited amount of time require students to become masters of their own education. To practice learning independently, begin to study the first few topics of Calculus. You are free to use any resources you want in order to master the topics listed below. When you feel you are ready, complete the following problems. I have included the answers to the odd-numbered problems. Use these to help check your ics:LimitsOne-sided limitsInfinite limitsLimits at infinityFinding limits from a graphHelpful Sites: - p/c/986560CD1E2A2981. limx→2x2-4x-22. limx→3x2-4x+3x-33. limx→4x-4x4. limx→1x3-4x5. limx→0x2-x-2x2-2x6. limx→0sin3xx7. limx→06+x2-36x8. limx→4x-2x-49. limx→82x2-17x+88-x10. limx→-32x+22-4x+3Finding Limits from Graphs:6229351708150088900-196851. limx→3-f(x)2. limx→3f(x)3. limx→-2+f(x)4. limx→4f(x)5. limx→-2f(x)6. limx→0f(x)7. f-2=8. f3=1. limx→3-f(x)2. limx→3f(x)3. limx→-2+f(x)4. limx→4f(x)5. limx→-2f(x)6. limx→0f(x)7. f-2=8. f3=One-Sided Limits:gx=2x+5, x<3x3-8x+1, x>31. limx→3+g(x)2. limx→3-g(x)77533516637000Infinite Limits:fx=2x6+x gx=x+31+x2hx=x+7x2-41. limx→-6-f(x)2. limx→-6+f(x)3. limx→-6f(x)4. limx→-1-g(x)5. limx→-1+g(x)6. limx→-1g(x)7. limx→2-h(x)8. limx→2+h(x)9. limx→2h(x)Limits at Infinity:1. limx→∞4x7-18x3+92. limx→-∞4x7-18x3+93. limx→∞8-4x29x2+5x4. limx→-∞8-4x29x2+5x ................
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