Calculus Answers

𝑓(𝑥) = 𝑥

3 − 3𝑥

2

, 𝑥 ∈ [1, 3]

𝑓(𝑥) = 𝑥

3 − 12𝑥, 𝑥 ∈ [0, 4]

An unbounded discontinuous function with NO absolute maximum and NO

absolute minimum. Domain: ________________

A discontinuous function with an absolute maximum of _____ at 𝑥 =_____ and

no absolute minimum. Domain: ___________________

A continuous function with NO absolute maximum and no absolute

minimum. Domain: ____________________

𝒇(𝒙) = 𝐜𝐨𝐬(𝟐𝒙

𝟑 + 𝟏)

𝒉(𝒙) = 𝐥𝐨𝐠𝟒

(𝟐𝒙

𝟑 − 𝟑)

𝒄(𝒙) = 𝐥𝐧 𝒙

𝟑 − 𝟒

Integration by Parts Fractions

1.) ∫(8t^3 + 13)dt/(t+2)(4t^2+1)

2.) ∫(5x^2 -3x+ 18)dx/x(9-x^2) from 1 to 2

Integration by Parts Fractions

1.) ∫4dx/(x^4-1)

2.) ∫8dx/x(x^2+2)^2