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Let A be a nonempty set of real numbers. Prove that A is bounded in the sense of 1.3.1 if and only if there exists a positive real number K such that |x|<=K for all x in A.
1.3.1 Let F be an ordered field. A nonempty subset A of F is said to be:
bounded above if there exists an element K in F such that x <=K for all x in A.
bounded below if there exists an element k in F such that k<=x for all x in A.
bounded if it is both bounded above and bounded below.
unbounded if it is not bounded.
What is the two diagonals of the generic rectangle mean? What is the different without the two diagonals?
For which positive numbers 'a' (now considering all positive numbers) do you get a convergent integral when you attempt to calculate the area of 'R'? but for the volume of the solid obtained by rotating 'R' around the x-axis.
We will take steps to find the tangent line to the graph of f at the general point (x,f(x)), and use it to find a tangent line with a specific property.
A function of two variables f(x,y) is integrated over the square [0,2] x [-1,1]. ex: integral from 0 to 2 , integral from -1 to 1 f(x,y) dx dy. (I wanted to input integral symbols there but didn't know how).
A particle has position function r(t). If r'(t)=c x r(t), where c is a constant vector, describe the path of the particle.
Find the shortest path between the vertices a and z that passes through the vertex f in the weighted graph in Exercise 3 in Section 10.6.
Carol and David decide to play a game as follows: Carol draws and keeps a card from a shuffled pack number 1 to 6.
A man with a tibia length of 40 cm long should be about 176 cm tall, and a man with a 44 cm long tibia should be 188 cm tall. By letting x represent the length of the tibia and y the height of the person; write and equation of a line relating the ..
To prove summation formulae. Be sure to identify where you use the inductive hypothesis.
For example, a possible sequence of tosses could look like HHTTTHTHHTHH. What is the probability that the length of such a sequence is at most 10?
The school cafeteria serves pizza every sixth day and applesauce every eighth day if pizza and applesauce are both on the menu today in how many days will they both be on the menu again
This line is called a geodesic line. Apply the Law of Cosines for a spherical triangle to find the angle between Great Falls and Lemhi. How far did that explorers travel just to get that far?
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