Lower semi-continuous and convex function

These are problems that ask as to which values of a variable a function is a) convex and b) lower semi-continuous. Please see the attached file for the full question.

Metric spaces complete and incomplete

See attached Let X=(-1,1) be equipped with topology inherited from R...

Linear functionals /not continuous

On the attachment there is a mistake. it should be not continuous instead of not bounded. Thanks! Prove that there exists a linear functional f:C([0,1])-->that is not continuous...

Financial and managerial accounting

Discuss the role of the financial accounting and managerial accounting functions in organizations and some of their job responsibilities. What are some of the differences between the two and the type of reports they may each use?

Functions and Graphs : Sketching, Domain, Range and Asymptotes

Please see the attached file for the fully formatted problems. 1. The length of a rectangular field is 3 times its width. If fencing costs $12 per metre, express the cost, C, of fencing the field as a function of the width, w. 2. Draw a set of axes and then plot the graph of the function f(x) = 2x —4, for —3 ...continues

Logarithmic and Exponential Functions Please see the attached file for the fully formatted problems.

Please see the attached file for the fully formatted problems. 1. If y = c^x express x in terms of y. (c is a positive constant) 2. a) Sketch the graph of y = 5^x for —2 < x < 3, clearly showing the key features of this exponential function. (b) On the same graph, sketch the function y = log5 x. Explain the relationship ...continues

Quadratic functions

Please answer all attached questions with full solutions, working and answers. Thank You. Solve the quadratic equations below using the method indicated.

Finance : Net Profit, Cash-Flow Statements, ROE, ROA and Profit Margin

For the 12months ended December 31, 2005, Quintero Corporation Posted the following financial results: Sales of $96.8 million, cost of goods sold of $72.0 million, overhead expenses of $5.5 million, depreciation of $2.3 million, and interest expense of $7.0 million. During the Fiscal year, capital spending totaled $97.8 millio ...continues

Complete metric space, open and dense

Let X be a complete metric space....

Normed space, parallelogram identity

Let X be a normed space. Suppose that for all {x,y} in X the parallelogram identity holds.....