Questions from General Calculus

Q: When money is spent on goods and services, those who receive

When money is spent on goods and services, those who receive the money also spend some of it. The people receiving some of the twice-spent money will spend some of that, and so on. Economists call thi...

Q: A certain ball has the property that each time it falls from

A certain ball has the property that each time it falls from a height h onto a hard, level surface, it rebounds to a height rh, where 0 < r < h. Suppose that the ball is dropped from an initial height...

Q: Suppose you know that {an} is a decreasing sequence and

Suppose you know that {an} is a decreasing sequence and all its terms lie between the numbers 5 and 8. Explain why the sequence has a limit. What can you say about the value of the limit?

Q: A sequence {an} is given by a1 = √2

A sequence {an} is given by a1 = √2, an+1 = √2 + an. (a). By induction or otherwise, show that is increasing and bounded above by 3. Apply the Monotonic Sequence Theorem to show that lim n→∞ an exists...

Q: Find at least 10 partial sums of the series. Graph both

Find at least 10 partial sums of the series. Graph both the sequence of terms and the sequence of partial sums on the same screen. Does it appear that the series is convergent or divergent? If it is c...

Q: Show that the sequence defined by is increasing and an < 3

Show that the sequence defined by is increasing and an

Q: Graph the curves y = xn, 0 < x < 1

Graph the curves y = xn, 0

Q: The figure shows two circles C and D of radius 1 that

The figure shows two circles C and D of radius 1 that touch at P. Tis a common tangent line; C1 is the circle that touches C, D, and T; C2 is the circle that touches C, D, and C1; C3 is the circle tha...

Q: A right triangle ABC is given with ∠A = θ and

A right triangle ABC is given with ∠A = θ and |AC| = b. CD is drawn perpendicular to AB, DE, is drawn perpendicular to BC, EF ⊥ AB, and this process is...

Q: The size of an undisturbed fish population has been modeled by the

The size of an undisturbed fish population has been modeled by the formula where Pn is the fish population after n years and a and b are positive constants that depend on the species and its environ...