Question 45629

Verified

Calculus

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

Question 45628

Verified

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

Verified

Calculus

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

Question 45477

Verified

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

Verified

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

Verified

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

Verified

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

Verified

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

Verified

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

Verified

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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