Motion
Random
Related Rates
Linearization
L'Hospitals
100
No Calc
A particle moves along the x-axis. The function x(t) gives the particle's position at any time t≥0
x(t)=t4-2t2-4
What is the particle's velocity v(t)at t=1?
0
100
The number of bones in a shark's body
What is 0?
100
No Calc
Ohm’s law states that if the resistance of the path of current between two points is constant, then the voltage difference V between the points and the current I flowing between the points, measured in amperes, satisfy the relationship V=cI, where c is a constant. Which of the following best describes the relationship between the rate of change with respect to time t of the voltage and the rate of change with respect to time t of the current?
dv/dt=c(dI/dt)
100
No Calc
The line tangent to the graph of the twice-differentiable function f at the point x=3 is used to approximate the value of f(3.25). Which of the following statements guarantees that the tangent line approximation at x=3.25 is an underestimate of f(3.25) ?
The function f is decreasing on the interval 3≤x≤3.25
B
The function f is increasing on the interval 3≤x≤3.25
C
The graph of the function f is concave down on the interval 3≤x≤3.25
D
The graph of the function ff is concave up on the interval 3≤x≤3.25
D
100
No Calc
limx→0 x2/(1−cosx) is
2
200
No Calc
A particle moves along the x-axis. The graph of the particle’s velocity v(t) at time t is shown above for 0<t<4.5. How many times does the particle change direction over the time interval 0<t<4.5 ?
Two times
200
The colors of the Norwegian flag
What is red, white and blue?
200
No Calc
A triangle has base b centimeters and height h centimeters, where the height is three times the base. Both b and h are functions of time t, measured in seconds. If A represents the area of the triangle, which of the following gives the rate of change of A with respect to t ?
dA/dt=3b(db/dt)cm2/sec
200
No Calc
The locally linear approximation of the differentiable function f at x=3 is used to approximate the value of f(3.2). The approximation at x=3.2 is an overestimate of the corresponding function value at x=3.2. Which of the following could be the graph of f?
A:
B:
C:
D:
D
200
Which of the following limits does not yield an indeterminate form?
A
limx→0 4x3/(cos(x)−1)
B
limx→3 ln(x/3)/(x2−7x+12)
C
limx→π (π−x)/(sin(2x)−1)
D
limx→∞ x10/(e2x+x)
C
300
A group of crows are known as this
What is a murder?
300
No Calc
A particle moves on the circle x2+y2=100 in the xy-plane for time t≥0. At the time when the particle is at the point (8,6), the value of dx/dt is 5. What is the value of dy/dt at this time?
dy/dt=-20/3
300
No Calc
The function f is twice differentiable with f(2) = 1 f′(2) = 4 , and f″(2) = 3 . What is the value of the approximation of f(1.9) using the line tangent to the graph of f at x = 2 ?
1.4
300
x = 2
f(x) = 4
f'(x)=3
g(x) = 2
g'(x) = 1
Selected values of the twice-differentiable functions f and g and their derivatives are given in the table above. The value of limx→2 (x2f(x)−16)/(g(x)−2) is
28
400
No Calc
A particle moves along the y-axis so that at time t≥0 its position is given by y(t)=(2/3t3)-5t2+8t. Over the time interval 0<t<5, for what values of t is the speed of the particle increasing?
0<t<1 and 4<t<5
400
The number of time zones in the world
What is 24?
400
No Calc
A 10-foot ladder is leaning straight up against a wall when a person begins pulling the base of the ladder away from the wall at the rate of 1 foot per second. Which of the following is true about the distance between the top of the ladder and the ground when the base of the ladder is 9 feet from the wall?
The distance is decreasing at a rate of 9/(√19) feet per second.
400
No Calc
Let f be the function given by f(x) = 2 cos x + 1. What is the approximation for f(1.5) found by using the line tangent to the graph of f at x = π/2 ?
π-2
400
No Calc
The figure above shows the graph of the twice-differentiable function f and the line tangent to the graph of f at the point (0,2). The value of
limx→0 (f(x)e-x−2)/(x2−2x) is
2
500
limx→∞ (ln(e3x+x))/x=
3