Anti-Derivatives
∫1/x dx
ln|x| + C
Use U-Sub
∫(3x+2)999 dx
1/3000 (3x+2)1000 +C
How many bones are in the cranium?
8 bones
(Frontal, Parietal, Temporal, Occipital, Sphenoid, Ethmoid)
Find the interval in which the function f(x) is increasing or decreasing.
f(x) = 5x2 - 2x + 3
Inc: (1/5, ∞ )
Dec: (-∞ , 1/5)
Expand:
log6((x4y8)/(z7w5))
4 log6(x) + 8 log6(y) - 7 log6(z) - 5 log6(w)
Find the C of F(x) using the point (1,6)
f'(x)=∫3 dx
F(x) = 3x + 3
Use U-Sub
∫x2(3-10x3)4 dx
- ((3-10x3)5/150) + C
Other than the US military, who owns the most explosives in the US?
Disneyland
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))
∫4x + 5x2 - ex dx
4x2/2 + 5x3/3 - ex + C
Use IBP
∫xe-2x dx
(xe-2x/-2) - (e-2x/4) + C
The only continent with no active volcanoes.
Australia
Transform this Semi-Log....
y=10(3t)
log3 y = log310 + t
∫x2(x2 + 1/x3 - 2) dx
x5/5 + ln|x| - 2x3/3 + C
Use IBP
∫te3t+t dx
(1/3) te3t+t - (1/9) e3t+t + C
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))
Transform this Semi-Log....
y=7(4t)
log4y = log47 + t
∫√(x) + 3) dx
2x3/2/3 + 3x + C
DOUBLE POINTS:
What object did the Mayans cover in natural rubber to make a ball for games?
Human Heads
Who is the SI Leader's FAVORITE Spider-man?
Miguel O'Hara
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·at that models the population, p, of rabbits t years after 2010...
p(t) = 850(1.126)t