Questions from General Calculus

Q: In the study of ecosystems, predator-prey models are often

In the study of ecosystems, predator-prey models are often used to study the interaction between species. Consider populations of tundra wolves, given by W (t), and caribou, given by C (t), in norther...

Q: If x2 + xy + y3 = 1, find the value

If x2 + xy + y3 = 1, find the value of y" at the point where x = 1.

Q: (a). Find the average rate of change of the area

(a). Find the average rate of change of the area of a circle with respect to its radius r as r changes from (i). 2 to 3 (ii). 2 to 2.5 (iii). 2 to 2.1 (b). Find the instantaneous rate of change when...

Q: In Example 4 in Section 1.3 we arrived at a

In Example 4 in Section 1.3 we arrived at a model for the length of daylight (in hours) in Philadelphia on the tth day of the year: Use this model to compare how the number of hours of daylight is i...

Q: The motion of a spring that is subject to a frictional force

The motion of a spring that is subject to a frictional force or a damping force (such as a shock absorber in a car) is often modeled by the product of an exponential function and a sine or cosine func...

Q: Under certain circumstances a rumor spreads according to the Equation P (

Under certain circumstances a rumor spreads according to the Equation P (t) = 1/1 + ae-kt where P (t) is the proportion of the population that knows the rumor at time t and a and k are positive consta...

Q: A particle moves along a straight line with displacement s (t

A particle moves along a straight line with displacement s (t) velocity v (t), and acceleration a (t). Show that a (t) = v (t) = dv/ds Explain the difference between the meanings of the derivatives dv...

Q: Air is being pumped into a spherical weather balloon. At any

Air is being pumped into a spherical weather balloon. At any time t, the volume of the balloon is V (t) and its radius is r (t). (a). What do the derivatives dV/dr and dV/dt represent? (b). Express dV...

Q: The flash unit on a camera operates by storing charge on a

The flash unit on a camera operates by storing charge on a capacitor and releasing it suddenly when the flash is set off. The following data describe the charge Q remaining on the capacitor (measured...

Q: Find equations of the tangent line and normal line to the curve

Find equations of the tangent line and normal line to the curve at the given point. y = (1 + 2x)2 (1, 9)