Exponentials and Logarithms
The value of 49^(-1/2)
What is
1/7?
The exact value of sin((7pi)/6).
What is
-1/2?
int3x^2-5dx
What is
x^3-5x+c
The number of arrangements in a row on a letter if 3 stamps are chosen from 7 different stamps.
What is 210?
The equation of the asymptote of the graph of y=2-3^(-x).
What is
y=2?
The amplitude and period of y=-3cos(x/2).
What is 3 and
4pi.
The average rate of change of f(x)=x^2-x over the interval [-1, 1].
What is -1?
For independent events A and B, the Pr(A nn B') if Pr(A)=0.6 and Pr(B)=0.2.
What is 0.48?
The value of b when log_b5+3log_b2-log_b10=2.
What is 2?
The minimum depth of water if the depth of water t hours after midnight in metres on any particular day is given by d(t)=6+2cos(pi/12t).
What is 4 metres?
The value of a if there is a stationary point at x=2 on the curve f(x)=3x^2+ax+3.
What is -12?
The number of different pairs if two people are chosen from a group of 8.
What is 28?
The range of the function f:(0, oo)->R, f(x)=2log_2(x+2)-1.
What is
x > 1 or (1, oo)?
The value of cos(x) if sinx=2/3 and pi/2 <=x<pi.
What is
-sqrt(5)/3?
f'(1) if f(x)=1/(3x+1)^2.
What is
-3/32?
The number of sets of three digits chosen from {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} such that exactly two of the digits are divisible by 3.
What is 21?
The inverse of the function g(x)=4log_2(5-x).
What is
g^-1(x)=5-2^(x/4).
The solution(s) of 4sin(2x)-4=0, 0<=x<=2pi.
What is
pi/4 and (5pi)/4?
The x-coordinate of the point on the curve f(x)=x^2-4x whose tangent line is perpendicular to the line with equation x-2y=3 .
What is
x=1?
Can use CAS. The probability of rain on a day in November is independent of rain on any other day and is 0.2. The probability of at most 8 rainy days in November (to 4 decimal places).
What is 0.8713?