Intermediate Mathematical Methods (Sequences and continuity)

| August 22, 2015

Intermediate Mathematical Methods (Sequences and continuity)

Answer all parts of all questions
1. By constructing a suitable sequence {xn} to the transition point, discuss whether the function is (i) continuous (ii) C1 or (iii) Ck where k > 1. (3 X 10 marks)
a.    f(x) = x2 +1 if x <1 = 3 if x = 1 ?
b.    f(x) = x2 +1 if x <1 = 2 if x = 1 ?
c.    f(x) = x2 +1 if x <1 = 2x if x = 1 ?
2. Consider the function f(x,y) = 2x2y/(x4+y4). Show that f1(t) = f(t,a) and f2(t) = f(a,t) are continuous functions of t for each fixed a. Show that f itself is not continuous at (0,0). [Hint: Take a sequence on the diagonal] (20 marks)

Get a 5 % discount on an order above $ 150
Use the following coupon code :
The restaurant Mr Wong from MERIVALE GROUP
model up Question 1: Undertake the Roller bracket exercise as detailed in section 3 of the Tutorial exercise book. You will need to create part models of all the components that make up the Roller Bracket device as well as the Roller Bracket assembly model. Also create a simple detail engineering drawing of the Base part. For this drawing you are required to show appropriate orthographic views, with dimensions, and a 3D view. You do not have to include tolerances and surface finishes but you should include a drawing sheet border and a completed title block. Question 2: Background Figure 1 depicts a foot-operated pump commonly used for inflating pneumatic tyres. The drawings that follow are for the various components making up the pump. The drawings are not reproduced to the same scale and some drawings are not fully dimensioned. The pump could be provided with one of two different pressure gauges – one having a Ø50 mm body and the other a Ø60 mm body. It is desirable to have a clearance gap of 3 mm between the gauge and the cylinder, see figure 1, irrespective of what gauge is used. To accomplish this you need to set up a parametric relationship between the gauge body and the dimension marked with * in the Fitting drawing of figure 5. Now, if the gauge body dimension is changed then the * dimension of the Fitting is automatically updated and the 3 mm gap between the gauge and cylinder is maintained. The Project Your task is to model up the various pump components and the assembled pump. More specifically you are required to: 1. Create parametric feature-based solid models for all the components, either shown or listed in the following pages. 2. Create an assembly model showing all parts in their working position when the return Spring is compressed to an overall length of 44 mm and the pump is fitted with the Ø50 Pressure gauge. 3. Set up a parametric relationship between the Pressure gauge and its Fitting that will preserve the 3 mm gap as described in the background section above. Guidance on the Project You will be expected to combine some research with sound practical judgement to obtain missing details in the information given and the drawings provided. Before commencing this assignment you should think about the function of each feature and each part and how the individual components might be made. Also consider the physical assembly process i.e. how the parts actually fit together and the order in which the components might be put together. Your model creation process should reflect this wherever possible. Some guidance is given in the instructions for the Roller Bracket exercise. The flexible hose does not have to be modelled. The Pressure gauge and the piston Valve models need only be representative of their physical shape and size as shown in the drawings provided. What and how you need to submit Your assignment is to be submitted in a compressed (zipped) folder for each question . For question 1, submit one compressed folder with: • Electronic copies of all the Creo3.0 models - i.e. part ‘.prt’ files and assembly ‘.asm’ files* • An electronic copy of a ‘.pdf ‘ file for the Base drawing. • An electronic copy of an A4 sheet (in .pdf format created from a word document) with a listing of the file names you used for each part and each assembly. For question 2, submit one compressed folder with: • Electronic copies of all the Creo3.0 models - i.e. part ‘.prt’ files and assembly ‘.asm’ files* • An electronic copy of an A4 sheet (in .pdf format created from a word document) with: A listing of the file names you used for each part and each assembly and Instructions on how to ‘test’ the parametric relationships between the Pressure gauge and its Fitting. Check that all files, in particular the assembly files, open correctly from your compressed folder before submitting it. It is very important that you do this as a marks penalty will apply if the files cannot be readily accessed by the markers. *If you use a program other than PTC Creo3.0 parametric you will need to convert your files to Creo ‘.prt’ and ‘.asm’ files. If your software does not support this conversion then save or export them as IGES or STEP files. Either way you should also submit all original / native model files - e.g. if you use Solid Edge then you would need to submit the Solid Edge files as well as the IGES or STEP files. You must also include screenshots (in ‘.pdf ‘ format) of the model / feature tree directories so that your model creation process can be assessed. Submit all these files in a single compressed folder for each question. You will also need to include a detailed account of how you set up the parametric relationship and how to test it. Figure 1: Foot-operated pump Figure 2: Pump details Figure 3: Pump details Figure 4: Pump details Figure 5: Pump details Figure 6: Pump details

Category: Essays

Our Services:
Order a customized paper today!