Gearing up for the test

Gearing Up by icathing

Greater Boston can be approximated by a semicircle of radius 8 miles with its centre on the coast. Moving away from the centre along a radius, the population density is constant for the first mile. Beyond that, the density starts to decrease according to the data given in the table, where ρ(r), thousands/mile , is the population density at a distance r miles from the centre.

(a) Using this data and a Riemann sum, estimate the total population living in the 8 mile radius.

(b) Determine a possible formula for ρ(r). Use this formula to make another estimate of the population.

2

(a) Using this data and a Riemann sum, estimate the total population living in the 8 mile radius.

HOMEWORK

(a) Using this data and a Riemann sum, estimate the total population living in the 8 mile radius.

HOMEWORK

Greater Boston can be approximated by a semicircle of radius 8 miles with its centre on the coast. Moving away from the centre along a radius, the population density is constant for the first mile. Beyond that, the density starts to decrease according to the data given in the table, where ρ(r), thousands/mile , is the population density at a distance r miles from the centre.

(b) Determine a possible formula for ρ(r). Use this formula to make another estimate of the population.

2

THE

RESTOFTHESEAREHOMEWORK

These are the correct answers, although they are not necessarily

in the correct order. ;-)

Now let's practice what we've learned ...Find the average value of ƒ on the given interval.

Sketch the graph of ƒ and a rectangle whose area is the same as the area under the graph of ƒ.

Find c such that ƒ = ƒ(c).ave

ƒ(x) = 2x, [0, 3]

Now let's practice what we've learned ...Find the average value of ƒ on the given interval.

Sketch the graph of ƒ and a rectangle whose area is the same as the area under the graph of ƒ.

Find c such that ƒ = ƒ(c).ave

Consider the region P bounded by the graph of the function ƒ between x=-8 and x=-5.

Set up, but do not evaluate, the integral that represents the volume of the solid generated by revolving P about:

(a) the y-axis. (b) the line x=-10. (c) the line x=3.

Now let's practice what we've learned ...Find the average value of ƒ on the given interval.

Sketch the graph of ƒ and a rectangle whose area is the same as the area under the graph of ƒ.

Find c such that ƒ = ƒ(c).ave

ƒ(x) = x + 2x - 5, [-2, 2]2