Determine whether the sequence is increasing, decreasing, or not monotonic. Is the sequence bounded?

$$an = n/n^2+1$$

In Exercise, use $a _ { n + 1 } / a _ { n }$ to show that the given sequence $\left\{ a _ { n } \right\}$ is strictly increasing or strictly decreasing.

$$\left\{ n e ^ { - n } \right\} _ { n = 1 } ^ { + \infty }$$

In Exercise, use $a _ { n + 1 } / a _ { n }$ to show that the given sequence $\left\{ a _ { n } \right\}$ is strictly increasing or strictly decreasing.

$$\left\{ \frac { 2 ^ { n } } { 1 + 2 ^ { n } } \right\} _ { n = 1 } ^ { + \infty }$$

The first few terms of a sequence

$$(x_n)$$

are given below. Assuming that the "natural pattern" indicated by these terms persists, give a formula for the nth term

$$x_n.$$

(a) 5, 7, 9, 11,···, (b) 1/2, -1/4, 1/8, -1/16,···, (c) 1/2, 2/3, 3/4, 4/5,···, (d) 1, 4, 9, 16,···.

Determine whether the sequence is increasing, decreasing, or not monotonic. Is the sequence bounded? $a_{n}=\cos n$

A body of mass m moves in a horizontal direction such that at time t its position is given by

$$x(t) = at^4 + bt^3 + ct,$$

where a, b, and c are constants. (a) What is the acceleration of the body? (b) What is the time-dependent force acting on the body?

If the sprinter from the previous problem accelerates at that rate for $20.00 \mathrm{~m}$ and then maintains that velocity for the remainder of a 100.00-m dash, what will her time be for the race?

An object is dropped from a roof of a building of height h. During the last second of its descent, it drops a distance h/3. Calculate the height of the building.

An object has an acceleration of +1.2 cm/s². At t = 4.0 s, its velocity is -3.4 cm/s. Determine the object's velocities at t = 1.0 s and t = 6.0 s.

Sketch the domain of f. Use solid lines for portions of the boundary included in the domain and dashed lines for portions not included.

$$f ( x , y ) = \frac { 1 } { x - y ^ { 2 } }$$

Find the exact value of each expression. sin(2 sin^-1(3/5))

What is wrong with the following calculation? 0 = 0 + 0 + 0 + ... = (1-1)+(1-1)+(1-1)+... =1-1+1-1+1-1+... =1+(-1+1)+(-1+1)+(-1+1)+... =1+0+0+0+...=1 (Guido Ubaldus thought that this proved the existence of God because “something has been created out of nothing.”)

Find the exact value of each expression.

$$tan(sec-^1)4$$

Determine whether the sequence is increasing, decreasing, or not monotonic. Is the sequence bounded? an = ne^-n