Show:
That Weird Squiggly Thing That looks like an S
Derive me to the store please
Insert Mean Girls quote here
Another squiggly rotated around a straight line
Other stuff that I don't have creative names for!
100
∫(sin x − cos x)dx
− cos x − sin x +C
100
x^3 + 3x^2 + 4x − 2
3x^2 + 6x + 4
100
lim x -> 3 of (5x^2 - 8x - 13) / (x^2 - 5)
2
100
y= (1/2)x from 0 to 5 about the x-axis
19.634 units^3
100
is this an example of exponential growth or decay? y= 20(1+ .5)^12
exponential growth
200
∫1/x dx
ln x +C
200
DAILY DOUBLE! 4 ln(x^2 + 1)
(8x)/(1+x^2)
200
lim x -> 0 of Sin(5x) / (3x)
5/3
200
y= x^3 -2x -4 from 0 to 2 about the x-axis
-25.132 units^3
200
A bank account balance, b, for an account starting with s dollars, earning an annual interest rate, r, and left untouched for n years can be calculated as b=s(1+r)^n (an exponential growth formula). Find a bank account balance to the nearest dollar, if the account starts with $100, has an annual rate of 4%, and the money left in the account for 12 years.
$160
300
∫(x +1)^6dx
[(x+1)^7]/ 7 + C
300
(x^3 − 7x) / (4x^2 − 3)
(4x^4 + 19x^2 + 21) / [(4x^2 − 3)^2]
300
lim x-> ∞ of 100 / (x^2 + 5)
0
300
y = x^2 – 2x, y = 8; about the line y = 8
1296pi/5 units^3
300
DAILY DOUBLE! For this exercise, the units on time t will be hours, because the growth is being measured in terms of hours. The beginning amount P is the amount at time t = 0, so, for this problem, P = 100. The ending amount is A = 450 at t = 6. A=Pe^rt
r = 0.250
400
∫ xe^(2x)dx
(1/2)x^2e^(2x) - (1/4)e^(2x) + C
400
(3x^3 − 3)10x^2
(96x^4 − 6x)[(3x^3 − 3)^9]
400
lim x -> ∞ of (x^4 + 5x^2 + 1)
∞
400
y = x2, x2 + y2 = 2; about the line y = –2
2pi^2 + 64pi/15 units^3
400
Find the inverse. f(x) = 6 - x/2
f^-1(x) = 12 - 2x.
500
∫sin^2 xdx
-(1/2)sinxcosx + (1/2)x + C
500
ln(ln(x^2 − 1))
(2X) / [(x^2 − 1) ln(x^2 − 1)]
500
lim x -> ∞ of (7x^2 + x - 100) / (2x^2 - 5x)
7/2
500
Find the volume of solid of revolution, when a right triangle with base 5 cm and height 10 cm is rotated about its height.
261.67 cubic centimeters
500
Find two nonnegative numbers whose sum is 9 and so that the product of one number and the square of the other number is a maximum.
x=9 or x=3 .