Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit

School of Mathematics and Statistics

Assignment 2

MATH1021: Calculus of one variable

Semester 2, 2021

This assignment is worth 8% of your final assessment for this course. Your answers should be well written, neat, thoughtful, mathematically concise, and a pleasure to read. Please cite any resources used and show all working. Present your arguments clearly using words of explana-tion, and diagrams where relevant. Mathematics is about communicating your ideas. This is a worthwhile skill which takes time and effort to master. The marker will give you feedback and allocate an overall letter grade and mark to your assignment using the following criteria:

Assignment Questions

1. Find the following limits. Justify your working carefully.

2. Consider the function

3. Consider the function

4. Write down the degree 5 Taylor polynomial for sin x, expanded about x = 0. Find an approximation for sin(−0.5). Use the remainder term R5(x) to show that this approx-imation is accurate to 4 decimal places. Show all working and explain your reasoning carefully.

5. Construct upper and lower Riemann sums with 8 equal subintervals to approximate the definite integral

How accurate is this approximation? Note that is an increasing function on [0, 2]. How many subintervals are required for an approximation to this integral that is accurate to within 0.01 of the true value?