Find an example of a sequence of continuous functions on fn on [0,1] such that the series...converges uniformly on [0,1] but the series ... diverges. Is it a counterexample for the Weierstrass test? ---
Prove the following theorem. Let f1,f2,f3.... be continuous functions on a closed bounded interval [a,b] . Then fn--->f uniformly on [a,b] if and only if fn(x)-->f(x) for every xn-->x such that xn,x E[a,b] . Please see the attached file for the fully formatted problems.
Consider the function f(x) = 2sinx + e^-x - 1 on the interval r E [?2,2]. If you plot the function, you will see that it has two roots on this interval (a) Write down a first order fixed point method for finding one of the two roots. (b) Will this fixed point method converge for both of the roots (Justify)? If it does not co
Show that the function f(x) = √x is uniformly continuous on [0,∞). Note: This is from a beginning analysis class. We can only use the definition of uniform continuity. (In other words, cannot use compactness, etc to prove) ---
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1. Find the distance from the origin to the line passing through the point P(3,1,5) and having the direction vector v=2i-j+k. 2. Graph z=x^2 in space.
Using graphing to check your answers is helpful. When you factor a trinomial into two binomials, each binomial represents a linear relationship. If you plot the two binomials (which are just lines) on a graph, what do they have in common with a plot of the trinomial itself? More important than that, how can this information be u
Independence and relations Real Analysis Jacobians (II) If u = (x + y)/z, v = (y + z)/x, w = y(x + y + z)/xz Show that u,v,w are not independent. Also find the
Suppose u(x) : X--> R v(x) : X --> R Both u(x) and v(x) are measurable Let f(x) : x --> R^2 f(x) = (u(x), v(x) ) Then f (x) is measurable Now prove a generalization of the above. That is, prove: if u_1(x) : X--> R u_2(x): X--> R . . . . u_n(x) : X--> R u_1,.
(See attached file for full problem description) Let a sequence xn be defined inductively by . Suppose that as and . Show that . (Note that " " refers to "little oh") HINT: Use the Mean-Value Theorem and assume that F is a continuously differentiable function.
In the real world, what might be a situation where it is preferable for the data to form a relation but not a function? There is a formula that converts temperature in degrees Celsius to temperature in degrees Fahrenheit. You are given the following data points: Fahrenheit Celsius Freezing point of water 32 0 Boiling
You have been invited to present statistical information at a conference. To prepare, you must perform the following tasks: 1. The following data was retrieved from www.cdc.gov. It represents the number of deaths in the United States due to heart Disease and cancer in each of the years; 1985, 1990, 1995, and 2002. Year Di
1. Graph for the function: f(x)=2-4^x 2. Solve for x: ln(7x-1)=6 3. Solve for x: lnx=3+ln(x-1) 4. Are the following funtions inverses of each other? 1. f(x)=x-1/3 g(x)=3x-1.
You have been invited to present statistical information at a conference. To prepare, you must perform the following tasks: 1.The following data was retrieved from www.cdc.gov. It represents the number of deaths in the United States due to heart Disease and cancer in each of the years; 1985, 1990, 1995, and 2002. Year
Differentiation of graphs for Celcius and Farenheit functions
Consider the following function: f(x) = 1/x for x in [1, infinity) = 1 for x in (-1,1) = -1/x for x in (-infinity, -1] Please explain why f(x) is in L^2(R)L^1(R)
How do I write z=6(cospi/3+i sinpi/3) in rectangular form?
What are the first four terms of the sequence whose general term is An=4(n-1)!/n!?
Find V in cylindrical polar coordinates. Is my working correct? (See attached file for full problem description).
Express the potential function U in cylindrical polar coordinates.. U(x,y,z) = -z(x^2+y^2)^2
If g(x) is even and h(x) is odd, what is g(h(x))? what about h(g(x))?
I have an answer for this problem, so it is just a check and confirmation I require. --- (See attached file for full problem description)
Which one of the following is true A Carmichael number is: a) a 2 pseudo-prime b) a 3 pseudo-prime c) a 5 pseudo-prime d) All of the above e) None of the above f) Just (a) and (b)
Graph the linear equation for the indicated values of the independent variable.Show this on a Graph as well as the formula V=50n + 30, 0.1<= n <= 0.9
Hi. Is the statement below TRUE or FALSE. Why? Question : I have a connected weighted undirected graph G with a minimum spanning tree T. If I increase the weight of one edge, the new minimum spanning tree T' of the new graph G' differs from T in at most one edge.
0<=x<=300 0<=y<=12000 Sketch
(See attached file for full problem description) 1) a. Let f be defined on [a, b] by f(x) prove directly that f is measurable b. let E be measurable subset of R, and let f be measurable function on E Define the function f and f on E as follows: f (x) = max { f(x), 0}, and f (x) = max{ -f(x), 0}, 1b. prove directly t
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Graph: 4x + y >= 4 Solve: (x - 10)(x + 9) Factor: 10r3s2 + 25r2s2 - 15r2s3 Factor : 3x2 + 7x + 2 Solve - factoring: x2 - 2x - 3 = 0
Here is a question on finding the vertical asymptotes g(x)=x+3/x(x-3) Can you show me a horizontal asymptote as well? f(x)=12x/3x^2+1.