Answer: Use formal definitions to prove the limit

Classical Mechanics 0
Consider the cube balanced on a cylinder as described in Example 4.7 (page 130). Assuming that b < r, use the Lagrangian approach to find the angular frequency of small oscillations about the top. The simplest procedure is to make the small-angle approximations to before you differentiate to get Lagr

Physics for Scientists and Engineers: A Strategic Approach, Standard Edition (Chs 1-36) 4
You are watching a jet ski race. A racer speeds up from rest to 70 mph in just a few seconds, then continues at a constant speed. Draw a basic motion diagram of the jet ski, using images from the video, from 10 s before reaching top speed until 10 s afterward.

Campbell Biology 10
The oceans affect the biosphere in all of the following ways except a. producing a substantial amount of the biospheres oxygen. b. removing carbon dioxide from the atmosphere. c. moderating the climate of terrestrial biomes. d. regulating the pH of freshwater biomes and terrestrial groundwater

Elementary Statistics 13
Technology. In Exercises 912, test the given claim by using the display provided from technology. Use a 0.05 significance level. Identify the null and alternative hypotheses, test statistic, P-value (or range of P-values), or critical value(s), and state the final conclusion that addresses the origin

Advanced Engineering Mathematics 10
Find the trigonometric polynomial F(x) of the form (2) for which the square error with respect to the given f(x) on the interval \(-\pi<x<\pi\) is minimum. Compute the minimum value for \(N=1,2, \cdots, 5\) (or also for larger values if you have a CAS). \(f(x)=|x| \quad(-\pi<x<\pi)\)

Advanced Engineering Mathematics 10
Compute the minimum square error for \(f(x)=x / \pi(-\pi<x<\pi)\) and trigonometric polynomials of degree \(N=1, \cdots, 5\).

Biology: The Unity and Diversity of Life 15
Bluebirds are songbirds that, like wood ducks, nest in cavities in trees. European house sparrows, which have been introduced to North America, also nest in such cavities. Explain how the arrival of the house sparrows affected the carrying capacity for bluebirds. What affect would you expect this cha

Principles of Economics 9
Xavier opens up a lemonade stand for two hours. He spends $10 for ingredients and sells $60 worth of lemonade. In the same two hours, he could have mowed his neighbors lawn for $40. Xavier earns an accounting profit of _________ and an economic profit of _________. a. $50; $10 b. $90; $50 c. $10; $50