Show:
Find the Derivative/ Antiderviative
Optimization
Limits
Riemann Sums
Trivia
100
f(x) = ( 3x −2)( 2x +1)
What is f '(x) =12x −1
100
A builder needs to make a box with a square bottom and rectangular sides. The box has no top. If the material for the sides cost $2 per square foot, and the material for the bottom costs $4 per square foot, what is the largest volume box that the builder can make with $20?
What is √(250/54)
100
lim x^2-7x+10 x-2 x^2-4
What is -3/4
100
The graph of y = x2 + 1 with x between 0 and 2. Approximate a Riemann sum using four approximating sections
What is 4.75
100
What is this formula called a^2+b^2=c^2
What is Pythagorean theorem
200
Find the derivative f(x)=√x(x^2+1)
What is f'(x)=(5x√x)/(2)+(1)/(2√x)
200
Cutting squares out of each corner of a sheet of cardboard creates a box without a lid. If the cardboard sheet has dimensions of 80 cm x 50 cm, determine the size of each equally sized square to be removed from the cardboard sheets in order to maximize the volume of the resultant box.
What is x=10 and x=33.3
200
lim cos(x) x-0 x+2
What is 1/2
200
Consider the function f (x) = x^2 on the interval [0, 6] Compute the left Riemann sum for f on this interval with n = 100 subintervals.
What is 70.942
300
f(x)=e^(2/x) then f'(x)=
What is -2/x^2(e^(2/x))
300
Determine the sides of the largest isosceles triangle that can fit within a circle with a radius of 12 cm.
What is 12√3
300
limit (2x-1)(3-x) x-∞ (x-1)(x+3)
What is -2
300
The table below shows the velocity readings of a car taken every two hours course of ten hours of driving. Use a midpoint Riemann Sum with five equal subintervals to find the approximate distance traveled by the car during this ten hour interval. The TABLE time | velocity (hrs) | (mph) -------------------- 0 | 30 2 | 66 4 | 75 6 | 68 8 | 55 10 | 40
What is 608
300
Q: What mathematical symbol did math whiz Ferdinand von Lindemann determine to be a transcendental number in 1882
What is pi
400
f(x)= (x-1)(X^2+2)^3 What is f'(x)
What is (x^2+2)^2(7x^2-6x+2)
400
You want to run an underground power cable from a power station on one side of a river to a house on the other side, as in the diagram.The house is 5 miles downstream from the station, and the river has a constant width of 1 mile. It costs $1000 per mile to lay cable underground, and $3000 per mile to lay cable under water.How should you lay the cable to minimize the total cost, and what will the minimum cost be?
What is $7828.43
400
Limit 5x^4+8x^2 X-0 3x^4-16x^2
What is -1/2
400
aproximate f(x)=√x on the interval [0,2] using 4 trapzoids
What is 1.886
400
What number, a one followed by 100 zeros, was first used by nine-year-old Milton Sirotta in 1940?
What is Googol.
500
If f(x)=cos(3x), then f(π/9)=
What is (√3)/2
500
For what value(s) of x will the function f (x) = x 3 -2x 2 - 5x be largest on the interval [- 10, 10] ?
What is x=10
500
lim 650x^2+4x+1320 x-∞ x^3-88x^2
What is 0
500
t(hours) 0 .5 1 1.5 2 2.5 3 v(miles/hour) 32 30 16 22 20 24 26 A speedboat travels downstream on a river. Its speed v, in miles per hour, at certain times is given in the table above. Using a left Riemann sum, what is the approximation of the total distance traveled by the speedboat from t = .5 to t = 3?
What is 56miles
500
What is the name of an actual unit of time for 1/100th of a second.
What is jiffy