Random
Water is pumped into a tank at a rate of R(t) and is draining from the tank at a rate of D(t), each in gallons per minute. Which expression would indicate that the amount of water in the tank is increasing?
R(t)-D(t)>0
Derivative of 5sin(x)
5cos(x)
When a function is increasing, the 1st derivative is...
Positive
When is a function continuous?
1. f(c) is defined
2. The limit of f(x) as x approaches c exists
3. The limit is equal to f(c).
If r(x) = z(x)h(x), then r'(x)=
z'(x)h(x)+h'(x)z(x)
Derivative of cos(x)-tan(x)
-sin(x)-(sec(x))^2
When a function has a local minimum, the first derivative is...
Zero
What is IVT?
The IVT states that if a function is continuous on [a, b], and if L is any number between f(a) and f(b), then there must be a value, x = c, where a < c < b, such that f(c) = L
If g(x) = f-1(x), with f(8)=3 and g(7)=3, then g'(3) equals...
1/(f'(8))
Derivative of x2-5x
2
When a function is concave up, the 2nd derivative is...
Positive
∫sin(3x)dx
-3cos(3x)
The rate at which the amount of water in a tank is changing can be modeled by the positive function R(t). If at time t=1 there are 20 gallons of water in the tank, which expression can be used to find the total amount the water level has increased from time t=1 to t=4?
∫14R(t)dt
Derivative of 5x-cos(x)
5+sin(x)
If velocity and acceleration have the same sign, the particle is...
Speeding up
Selected values from the function f(x) are shown in the table below. When a right Riemann sum with two subintervals is used to approximate an integral, from 0 to 5, the value is
x | 0 | 3 | 5 |
f(x) | 4 | 1 | 4 |
11
For a particle moving along the x-axis, x(1)=7 and v(1)=2. At time t=1, it can be said that the particle is moving towards or away from the origin?
Moving away from the origin
Derivative of sin(x^2)*e^5
2xe^5 *cos(x^2)
The position, in meters, of a body of time t sec is s(t)=t^3 -6t^2 +9t. Find the body's acceleration each time the velocity is zero.
6 and -6
A right Riemann sum is an underestimate when the function is...
Decreasing