A
int(6x−4)(3x^2-4x)^5dx
1/6 (3x^2-4x)^6 + C
What is the phrase the teacher says to get attention?
Raise your hand if you can hear me
int 12x^2-6x dx
4x^3-3x^2+C
What is the capital of Australia?
Canberra
f'(x)=sec^2 x+1
f(x)= tan x + x +C
int (6x^2 - 5x^5 + 8x^3 + 4sqrtx) / (2x^3) dx
3ln |x| - 5/6x^3+4x-2/sqrtx+C
26
int sin(1/x)/x^2 dx
cos(1/x) + C
Which planet is known as the "Red Planet"?
Mars
Evaluate
int 3^(2x)/5dx
(3^(2x))/(10ln3)+C
∫18e^(3x)sqrt(e^(3x) −5) dx
4(e^(3x)-5)^(3/2) + C
What musical did the teacher saw last year?
Hamilton
The rate of change of the volume of a balloon is
(dV)/dt = 3t^2 + 2t
If initially the volume is 5 cm³, find the volume at time t.
V(t)=t^3+t^2+5
The chemical symbol for gold on the periodic table is:
Au
Evaluate
int cosx/(1+sin^2x) dx
arctan(sinx) +C
∫ [ 4 /t^2 tan ( 3/t ) sec ( 3/ t ) + 10^(2t) ] d t
-2/3 sec (3/t) + 10^(2t) / 2ln10 + C
When is the teacher birthday?
Evaluate
int x/(1+x^4) dx
1/2 arctan (x^2)+C
The Great Wall of China was primarily built to protect against invasions from which historical group?
The Mongols
The marginal cost to produce x items is
C'(x)=0.3x^2-2x+50
. If the fixed cost is $1000, find the cost function.
C(x)=0.1x^3 - x^2+50x +1000
∫12e3x[sec2(e3x)−2]dx
What are the teacher's favorite flowers?
Sunflower, tulips, Hydrangeas
The growth rate of a bacteria population is
(dP)/dt=15/(sqrt(2t+4)
bacteria/day. The initial population is 500. Find the population equation.
P(t)=15sqrt(2t+4) + 470
At the 2022 Grammy Awards, which album won "Album of the Year," making the artist the second ever to win this category three times?
*30* – Adele
Find f(x) if
f''(x)=2+12x^2, f'(0)= -1, and f(0)=5
f(x)=x^2+x^4 -x +5