Integration
Misc
Differentiation
Optimization
Limits
100
ʃ 5sec4xtan4x dx
What is 5/4 sec 4x +c ?
100

the least populated state in the country?

What is Wyoming ?

100
Differentiate y = sin^2(x)
What is 2sin(x)cos(x) ?
100
A rectangular box with a volume of 60 cubic ft has a square base. Find a function that models its surface area S in terms of the length x of one side of its base.
What is S(x)=2x^2+240/x
100
Find the limit as x approaches -3 of (x^2+x-6)/(x+3)
What is -5 ?
200
ʃ x sin(x²)dx
What is -1/2 cos x²+C
200
What dog breeds does Mr.Bart currently have. Bonus - Names!
What are saint bernard (Munson) and bernese mt dog (Mia)?
200
How do you tell if a particle is speeding up?
What is the velocity and the acceleration will have the same sign?
200
The total distance traveled from t = 1 to t = 3 if the a acceleration function a(t) = 12t - 4. At time t = 1, the velocity is v(1) = 7.
What is 46?
200
Find the limit as x approaches 0 when [(x+1)^(1/2)-1]/x
What is 1/2 ?
300
ʃ (sinx + cosx)²
What is x+ sin²x+c ?
300
DOUBLE BONUS:What former New York Yankee will have his number retired? and what is the number?
What is Derek Jeter. What is #2.
300
Find dy/dx of ytan(x+y) = 4
What is y/x ?
300
A rectangular box has a square base. Its height is half the width of the base. Find a function that models its volume V in terms of its width w.
What is V(w)=0.5w^3
300
Find the limit as x approaches 0 when (4sinx)/x
What is 4 ?
400
ʃ (cos5x)/ (3+ sin 5x) dx
What is (1/5)ln |3+sin 5x| +C
400
How many vertical asymptotes exist for the function f(x)= 1/ [2(sin x)^2 - sin x - 1] in the open interval 0 < x < 2pi ?
What is 3 ? [7pi/6, pi/2, 11pi/6]
400
f (x) = (e^x)/x
What is f ' (x) = (e^x)/x - (e^x)/(x^2)
400
Find two positive numbers whose product is 750 and for which the sum of one and 10 times the other is a minimum.
What is x=50sqrt3 y=5sqrt3
400
DOUBLE BONUS:What is lim x->-1+ (x^2+1)/(x^4-1)(x^2-1)
What is ∞ ?
500
The integral from 0 to x of the function sin(t) dt
What is -cos(x) + 1?
500

A rectangular box with a square base and no top is to have a volume of 108 cubic inches. Find the dimensions for the box that require the least amount of material.

What is length and width of 6 inches and a height of 3 inches.

500
Find dy/dx of 4x^2 - 9y^2 = 17
What is (4x)/(9y) ?
500
An open rectangular box with square base is to be made from 48 ft.2 of material. What dimensions will result in a box with the largest possible volume ?
What is x=4 ft. and y=2 ft. , and V = 32 ft.^3 is the largest possible volume of the box.
500
What is lim x->4- (x^2+4)/(sqrt(x+1))
What is 20/sqrt(5) or 4sqrt(5) ?
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