Question

Calculus

A graphing calculator is recommended.

A particle moves according to a law of motion s = f(t), t > 0, where t is measured in seconds and s in feet. (If an answer does not exist, enter DNE.)

f(t)=t^{3}-9 t^{2}+24 t

(a) Find the velocity (in ft/s) at time t.

(b) What is the velocity (in ft/s) after 1 second?

(c) When is the particle at rest? (Enter your answers as a comma-separated list.)

(d) When is the particle moving in the positive direction? (Enter your answer using interval notation.)

(e) Draw a diagram to illustrate the motion of the particle and use it to find the total distance (in ft) traveled during the first 6 seconds.

(f) Find the acceleration (in ft/s^2) at time t.

Find the acceleration (in ft/s^2) after 1 second.

(g) Graph the position, velocity, and acceleration functions for 0 <= t <= 6.

(h) When is the particle speeding up? (Enter your answer using interval notation.)

When is it slowing down?  Verified ### Question 45629  Calculus

III. The following Theorem was discussed in thesection about infinite series

### Question 45628  Calculus

II. The following figure shows an infinite zigzag path with each zag occurs at an angle of t/4. Find the total length of this infinite zigzag path.

### Question 45627  Calculus

I. Find the total area of the infinitely many triangles shown in the figure below.

### Question 45477  Calculus

The bandwidth of a video being delivered on the internet has a continuous distributionon the interval (0,4), with a probability density function (PDF)
f_{X}(x)=\left\{\begin{array}{ll} \frac{c}{(1+x)^{2}} & \text { for } 0<x<4 \\ 0 & \text { otherwise. } \end{array}\right.
What is the probability that the bandwidth of a video is less than 0.6.

### Question 45476  Calculus

You are given that P(A) = 0.5 and P(A U B) = 0.7. Student 1 assumes that A and B are independent and calculates P(B) based on that assumption. Student 2 assumes that A and B are mutually exclusive and calculates P(B) based on that assumption.Find the absolute difference between the two calculations.

### Question 45456  Calculus

\text { Sketch a (relatively decent) contour diagram for } f(x, y)=\frac{y+1}{x-y} \text { which includes the }
c= 0, 1, 2, –2 level curves. (Pick a reasonable scale for your axes.)

### Question 45455  Calculus

1. (3) Is there a function of two variables whose z = 0 level curve consists exactly of the circles x2 + y2 = 2 and x2 + y2= 9? If so, what is an example? If not, why not?

### Question 45454  Calculus

\text { a) Consider the sphere } S:(x-2)^{2}+(y+3)^{2}+(z-1)^{2}=16
(b) Let P be the horizontal plane which passes through (4, 5, 2). Find the equation ofthe circle where P intersects S.
(a) Find anequation for the circle where S intersects the xz-plane.
(c) Find the point(s) where S intersects the x-axis.

### Question 45453  Calculus

2. (5) Consider the (somewhat strange) function V (w) which returns the number of uniquevowels (a, e, i, o, u only) in the English word w.
(a) What is V(calculus)? V (brachiosaurus)?
(b) Describe (in words) the zeros of the function V, and giveexample.one
(c) What is the range of V?

### Question 45452  Calculus

\text { Consider the function } f(x, y)=x-y^{2}+3 \text {. Sketch the cross-section of } f(x, y) \text { with }
\text { (a) } x=2
\text { (b) } y=-1

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