?
lim_(x->0)(e^x-1)/(2x+1) = ?
0
The lion population on an island is modeled by P(t) = B(t) - D(t) , from 0<t<10, where t is in years. There are 15,000 lions on an island at t = 0. The birth rate is modeled by B(t) = 110e^(0.08t) and the death rate is D(t) = 80e^(0.2t) . Is the population increasing or decreasing at t = 2?
Increasing.
5 km
A box's volume is increasing by 20 cubic inches per second. If the length and width of the cube stay constant, the length being 4 inches, and the width being 2.5 inches, find the rate of change of the height in inches per second.
10 inches per second
This is Mr. Krieger's favorite Mathematician
L'Hopital!
lim_(x->0)(sin(x)/x)
1
For a differentiable function g(x), it is known that g(1) = 12, and g'(1) = -3. Use the tangent line approximation at x = 1.1 to estimate g(1.1)
g(1.1) ~ 11.7
Leaving New Buffalo High School, let Mr. Krieger be walking 2 km per hour north, and let L'Hopital be walking 3 km per hour east. Mr. Krieger has walked 4 km, L'hopital has walked 3 km, and the distance between them is 5 km. Find the rate of change of the distance between them.
17/5 km/hr or 3.4 km/hr
12pi (cm^3)/(min)
This is who is in the lead for L'Hopital...
Braedan
Let f be the function defined by f(x)= 2x+1 , and let g be a differentiable function with derivative given by g'(x)=1/x+15x . It is known that lim_(x->oo)g(x)=oo . Find the value of
lim_(x->oo)f(x)/g(x)
0
A person is doing jumping jacks during a workout. The amount of jumping jacks the person does is given by the function J(t), where t represents minutes. Give an interpretation of P'(2)=-14
The person's jumping jacks per minute is decreasing by 14 jumping jacks per minute at 2 minutes.
This is what calc is short for, as said on my board.
Calculator