Exam 4 Review

Anti-Derivatives

100

∫1/x dx

ln|x| + C

200

Find the C of F(x) using the point (1,6) 

f'(x)=∫3 dx

F(x) = 3x + 3

300

 ∫4x + 5x² - e^x dx

4x²/2 + 5x³/3 - e^x + C

400

 ∫x²(x² + 1/x³ - 2) dx

x⁵/5 + ln|x| - 2x³/3 + C

500

 ∫√(x) + 3) dx 

2x^3/2/3 + 3x + C

Substitution

100

Use U-Sub

∫(3x+2)⁹⁹⁹ dx 

1/3000 (3x+2)¹⁰⁰⁰ +C

200

Use U-Sub

∫x²(3-10x³)⁴ dx

- ((3-10x³)⁵/150) + C

300

Use IBP

∫xe^-2x dx

(xe^-2x/-2) - (e^-2x/4) + C

400

Use IBP

∫te^3t+t dx

(1/3) te^3t+t - (1/9) e^3t+t + C

500

DOUBLE POINTS:

What object did the Mayans cover in natural rubber to make a ball for games?

Human Heads

I'm the BEST!!!

100

How many bones are in the cranium?

8 bones

(Frontal, Parietal, Temporal, Occipital, Sphenoid, Ethmoid)

200

Other than the US military, who owns the most explosives in the US?

Disneyland

300

The only continent with no active volcanoes.

Australia

400

During development, there is a signaling molecule crucial to embryonic development. This protein is named after a famous video game character. 

Who is this character?

Sonic the Hedgehog

(The protein is called Sonic Hedgehog Protein (SHH))

500

Who is the SI Leader's FAVORITE Spider-man?

Miguel O'Hara

Testing Testing.

100

Find the interval in which the function f(x) is increasing or decreasing.

f(x) = 5x² - 2x + 3

Inc: (1/5, ∞ )

Dec: (-∞ , 1/5)

Logs

100

Expand:

log₆((x⁴y⁸)/(z⁷w⁵))

4 log₆(x) + 8 log₆(y) - 7 log₆(z) - 5 log₆(w)

200

Condense:

5 log₆(x+y) + 1/2 log₆(y) - 7 log₆(z) - 5 log₆(w-4):

log₆((sqrt(y)*(x+y)⁵)/(z⁷(w-4)⁵))

300

Transform this Semi-Log....

y=10(3^t)

log₃ y = log₃10 + t

400

Transform this Semi-Log....

y=7(4^t)

log₄y = log₄7 + t

500

Suppose that the rabbit population in a certain wildlife preserve is growing exponentially. In the year 2010, the population was 850, and in the year 2018, the population was 2200...

Find a function of the form p(t) = p₀·a^t that models the population, p, of rabbits t years after 2010...

p(t) = 850(1.126)^t