Series
Calculus
Counting
Algebra
100
Find the sum of the infinite geometric series: 4 + (4/7) + (4/49} + (4/343) + ...
14/3
100
Find the Limit
Lim→0 (x -1)/ x
DNE
100
Suppose a fair coin is randomly tossed for 75 times and it is found that head turns up 45 times and tail 30 times. What is the probability of getting a head?
45/75 or 0.6
100
Write the equation of the line that passes through the point (0, 0) and is perpendicular to the line shown below?
y = (5/4)x
200
The sum of an arithmetic series is 270. The common difference is 1 and the first term is 4. What is the number of terms in the series?
20
200
Evaluate the limit without using l’hopital rule.
Lim—>0 sin(3x)/5x
3/5
200
A group of 10 students is divided into two subgroups of 6 and 4. In how many ways can this be done?
(10C4)*(6C6) or 210
200
D
300
Determine the sum (S) of this infinite series. S = 1- ½ + ⅓ - ¼ + ⅕ - ⅙ +…
0.6931 or ln(2)
300
Find any one point of intersection between the inverse and the derivative of x^2 - x?
(1.39,1.781) or (0.36,-0.281)
300
Three dice are rolled. What is the probability that the sum of the numbers is a prime number?
73/216
300
One pipe can fill a tank in 8 minutes, a second pipe can fill it in 12 minutes and a third pipe can fill it in 24 minutes. If the tank is empty how long will it take the three pipes, operating together, to fill it?
4 minuites