AP Calculus BC – Memorization Exam
Questions and Answers
d/dx sin⁻¹x - Correct Answers -1/√(1-x²) not +/-1
d/dx cos⁻¹x - Correct Answers -⁻1/√(1−x²) not +/-1
d/dx tan⁻¹x - Correct Answers -1/(1+x²)
d/dx cot⁻¹x - Correct Answers --1/(1+x²)
d/dx sec⁻¹x - Correct Answers -1/(IxI√(x²-1)) not +/-1,0
d/dx csc⁻¹x - Correct Answers --1/(IxI√(x²-1)) not +/-1,0
d/dx sinx - Correct Answers -cosx
d/dx cosx - Correct Answers --sinx
d/dx tanx - Correct Answers -sec²x
d/dx cscx - Correct Answers --cscxcotx
d/dx secx - Correct Answers -secxtanx
d/dx cotx - Correct Answers --csc²x
3 factors of continuity - Correct Answers -1) f(c) exists
2) lim f(x) exists
x-->c
*does the limit from the right = limit from the left?*
3) #1 = #2
logistic differential equation - Correct Answers -dy/dt = ky(1-y)
logistic equation - Correct Answers -y = L/(1+be^-kt)
volume of a sphere - Correct Answers -(4/3)πr^3
surface area of a sphere - Correct Answers -4πr^2
Questions and Answers
d/dx sin⁻¹x - Correct Answers -1/√(1-x²) not +/-1
d/dx cos⁻¹x - Correct Answers -⁻1/√(1−x²) not +/-1
d/dx tan⁻¹x - Correct Answers -1/(1+x²)
d/dx cot⁻¹x - Correct Answers --1/(1+x²)
d/dx sec⁻¹x - Correct Answers -1/(IxI√(x²-1)) not +/-1,0
d/dx csc⁻¹x - Correct Answers --1/(IxI√(x²-1)) not +/-1,0
d/dx sinx - Correct Answers -cosx
d/dx cosx - Correct Answers --sinx
d/dx tanx - Correct Answers -sec²x
d/dx cscx - Correct Answers --cscxcotx
d/dx secx - Correct Answers -secxtanx
d/dx cotx - Correct Answers --csc²x
3 factors of continuity - Correct Answers -1) f(c) exists
2) lim f(x) exists
x-->c
*does the limit from the right = limit from the left?*
3) #1 = #2
logistic differential equation - Correct Answers -dy/dt = ky(1-y)
logistic equation - Correct Answers -y = L/(1+be^-kt)
volume of a sphere - Correct Answers -(4/3)πr^3
surface area of a sphere - Correct Answers -4πr^2
