(c)
(d)
(b)
(c)
(a)
(b)
(c)
(d)
(a)
(b)
(c)
(d)
(e)
(a)
(b)
(c)
(d)
to approximate tan−^1 1/5, and the polynomial of degree 1 to
approximate tan−^1 1/239.
Use part (b) to evaluate the expression in (a).
Explain how the approximation for π/4 given here compares with
that obtained using π/4 = tan−^1 1.
(a) Show that the series converges.
How many terms of the series are needed to get a partial sum within
0.1 of the sum of the whole series?
Tell whether the series is absolutely convergent,
conditionally convergent, or divergent. Justify your answer.
Given with y = 2 at t = 0 and y = 5 at t = 2:
Find k.
Express y as a function of t.
For what value of t will y = 8?
Describe the long-range behavior of y.
An object P is in motion in the first quadrant along the parabola y = 18 −
2 x^2 in such a way that at t sec the x-value of its position is .
Where is P when t = 4?
What is the vertical component of its velocity there?
At what rate is its distance from the origin changing then?
When does it hit the x-axis?
How far did it travel altogether?
A particle moves in the xy-plane in such a way that at any time t ≥ 0 its
position is given by x(t) = 4 arctan t, .
Sketch the path of the particle, indicating the direction of motion.
At what time t does the particle reach its highest point? Justify.
Find the coordinates of that highest point, and sketch the velocity
vector there.
Describe the long-term behavior of the particle.
Let R be the region bounded by the curve r = 2 + cos 2θ, as shown.
