1. Let f:R->R be uniformly continuous on R (the reals) and let f_n(x)=f(x+1/n) for x in the reals. Show that (f_n) converges uniformly on the reals to f.

2. Suppose that the sequence (f_n) converges uniformly to f on the set A, and suppose that each f_n is bounded on A. (That is, for each n there is a constant M_n such that |f_n(x)| < M_n for all x in A). Show that the function f is bounded on A.

3. Let f_n(x) = nx/(1+nx^2) for x in A =[0,infinity). Show that each f_n is bounded on A, but the point-wise limit f of the sequence is not bounded on A. Does (f_n) converge uniformly to f on A? Hint: f_n(1/squareroot(n))=squareroot(n)/2, where squareroot n= n^0.5.

4. Let f_n(x) =(x^n)/n for x in [0,1]. Show that for the sequence (f_n) of differentiable functions converges uniformly to a differentiable function f on [0,1], and that the sequence (f'_n) converges on [0,1] to a function g, but that g(1) does not equal f'(1).

Applicable corner points-maximize profit : A company makes two soft drinks A and B. Each liter of A requires 4 hours processing and 4 hours distillation while each liter of B requires 5 hours processing and 3 hours distillation. |

Transportation problem- cost minimization : Transportation problem: Cost minimization, Three quarries produce lime which is then shipped to five warehouses |

Preparing an income statement : Prepare an income statement through gross profit for the year ended December 31, 2004. |

How will the character of the income or loss be determined : The character of any income or loss will be ordinary if the contributed property is sold by the partnership within five years after the date of contribution regardless of the character of the asset in the hands of the partnership. |

Uniform continuity and boundedness : Let f:R->R be uniformly continuous on R (the reals) and let f_n(x)=f(x+1/n) for x in the reals. Show that (f_n) converges uniformly on the reals to f. |

Why does a business need to understand elasticity of demand : Why does a business need to understand elasticity of demand and calculate the elasticity of demand between prices $6 to $8 |

Jordan canonical form of matrix : If I treat the upper block as a 2x2 matrix, I can find P = [1 0; 1 1] (Note: Using Matlab notation here). This correctly results in INV(P)AP = [3 1; 0 3] which is in the form needed. |

Straight-line method of depreciation : A change from the straight-line method of depreciation to an accelerated method should be accounted for as a(n) |

Define youth as a consecutive of challenging : define Youth as a consecutive of challenging |

## Find a fire detection sensor is tested for its failure rateA fire detection sensor is tested for its failure rate and found to have a mean failure rate of 3.6E-2 per hour of exposure with a standard deviation of |

## Find the probability of the ten unit sampleFind the probability that all units in the ten unit sample will test satisfactory. |

## Estimation binomial distributionEstimation : Binomial Distribution Suppose T is a random variable such that |

## Interpreting graphs and charts in mathIn a percent change graph of an average teachers annual salary the bars representing successive years are either unchanged or decreasing in size. |

## How many permutations are there of 12 objectsHow many permutations are there of 12 objects taken five at a time? How is this answer related to answers in 1 and 2? |

## Calculate a probabilty of flushPoker, in the deck 52 cards, hand of 5 cards, one of the winning hands is flush, all cards belong to a common suit. A) Calculate the number of possible combinations of poker hands B) Calculate a probabilty of flush |

## Estimate the expected grade & variance for the courseEstimate the expected grade & variance for the course |

## Solve a system of equationsA major city car rental agency has a total of 2200 cars rented out of 3 locations: Metro Airport (m), Downtown Airport (d), and at smaller City Airport (c). |

## Find the probability of not seeing any moose in a dayIf the probability of seeing moose in a day in a certain region of Alaska is 0.47, what is the probability of not seeing any moose in a day there? |

## Second order differential equationConvert the nonlinear, second order differential equation to the first order system and solve the differential equation |

## Find the probability of twin birthsased upon statistical studies it has been found that 3.32% of all births in the United States will result in twins being born. If 17,300 births are selected at random what is the probability that: Find the Probability of Twin Births |

## Equations of straight linesA line passes through the point (6, -6) and has a slope of -3. Write an equation for this line in (x, y) coordinates. Write equations for the vertical and the horizontal lines passing through the point (6, 1) in (x,y) coordinates. |

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd