Real Analysis Answers

Is the following statements True or False? Please state your answer and explain them.
1) If a < L for every element in a set A, then sup A < L.
2) limit of (an) when n goest to infinity is L if and only if the limit of |an - L| when n goes to infinity is 0.

find the laplace transform of (e^-at -e^-bt)/t

_____24. A prismatoid has an upper base of 90% , a lower base of 2100% , an altitude of 100 cm, and a midsection of 120? . What is its volume? (WITH SOLUTION)

a) 7000 cm3 b) 11 500 cm3 c) 13 000 cm3 d) 17 500 cm3

_____25. Find the midsection of a frustum of a square pyramid if its lower base is 20 cm on a side, its upper base is 12 cm on a side, and the altitude of the frustum is 14 cm. (WITH SOLUTION)

a)144 cm2 b) 240 cm2 c) 256 cm2 d) 400cm2

The surface area of a sphere inscribed in a regular tetrahedron is 144 cm2 (with solution)

_____21. What is the radius of the sphere?

a) 12 cm b) 7cm. c) 6cm d) 5cm

_____22. What is the altitude of the tetrahedron?

a) 20cm b) 24cm. c) 28cm d) 48cm

If A={x∈Q,x<3} then find Sup(A)

Discuss order-completeness of the set of rational numbers

Consider the following sequence of successive numbers of the 2^k-th power: 1, 2^2^k, 3^2^k, 4^2^k, 5^2^k, … Show that the difference between the numbers in this sequence is odd for all k ∈ N?

f:[0,1]→R be Riemann integrable. Find lim┬(n→∞)⁡∫_0^1▒〖x^(n+1) f(x)dx〗.