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Simplification of linear algebraic expressions and expressions with fractional coefficients and solve x;
A new fashion in clothes is introduced. It spreads slowly through the population at first but then speeds up as more people become aware of it.
Recall that R^3={(x,y,z):x,y,z(subset of R)}. Let G(V,E) be a directed graph, in which V= {(x,y,z)-(subset of R^3) :x,y,z(subset of R),-10<=x,y,z<=10}.
Simplify the block diagram diagrams shown in Fig. below and obtain the transfer function C(s)/ R(s).
For a fixed rate, a fixed principal amount, and a fixed compounding cycle, the return is an exponential function of time.
Prove, from the definition of function (using ordered pairs), that composition of functions is associative. (i.e. prove that f * (g*h) = (f* g) *h)
Let f : R --> R be an additive function i.e. f(x+y) = f(x) + f(y) for all x,y in R.
A power Station and a factory are on opposite sides of a river 60m wide. A cable must be run from the power station to the factory.
Let G = (V, E) be a connected and undirected graph, and u is a chosen vertex in V.
What is the end behavior of this function? (Does it go up or down to the left? Does it go up or down the right?)
Think of one real situation that involves exponential growth and that involves exponential decay. for each example, your project should include the following:
Suppose that X and Y are finite sets, with m and n elements respectively. Suppose further that the function f : X ? Y is one-to-one and the function g : X ?Y
For the rational function (f) x = (2x2 + x - 6)/(x - 1)
Use the product rule to find the slope of the line tangent to the graph of the function.
Consider the functions f(x) = x^2 and g(x) = square root of x, both with domain and co-domain R+, the set of positive real numbers.
Show that a function f is measurable IF AND ONLY IF there exists a sequence (f_m) of set functions such that f(x)=lim f_m(x) for almost all x.
Show both analytically and graphically that f and g are inverses:
A logistics specialist for Wiethoff Inc. must distribute cases of parts from 3 factories to 3 assembly plants.
Graph each absolute value function and state its domain and range.
Let G be a self-complementary graph of order n, where n=1(mod 4).
Let v_1,v_2,...,v_k be k distinct vertices of a k-connected graph G. Let H be the graph formed from G by adding a new vertex of degree k that is adjacent
Prove that a nontrivial connected digraph D is Eulerian if and only if E(D) can be partitioned into subsets E_i , 1<=i<=k, where [E_i] is a cycle for each i.
Let G be a graph of diameter at least three. Can you find an upper bound on the diameter of the complement of G?
Let G be a simple graph with no isolated vertex and no induced subgraph with exactly two edges. Prove that G is a complete graph.
Show that if two vertices u and v have the same score in a tournament T, then u and v belong to the same strong component of T.