MZB101 - Modelling with introductory calculus Problem solving task - assessment description NOTE! At QUT, assessment submitted after the due date without an approved extension will not be marked and will receive a grade of 1 or 0%. If special circumstances prevent you from meeting the assessment due date, you can apply for an extension (see MZB101 Blackboard, \"Assessment\" section for a link to details/apply). If you don't have an approved extension you should submit the work you have completed by the due date and it will be marked. The Problem solving task is a single assessment item, but feedback is provided to you regularly throughout the semester to aid your learning and development of skills. As such, you need to submit responses throughout the semester also. Submission cutoffs and the associated questions are clearly indicated throughout this document. Total weight: 60% (comprised of 415% parts) Submissions and due dates: Throughout the semester, you will need to submit written problem solving attempts on four occasions (due weeks 3, 5, 7, 9). Specific submission dates are as follows: Part 1: Friday 17 March, 11.59pm Part 2: Friday 31 March, 11.59pm Part 3: Thursday 13 April, 11.59pm Part 4: Friday 5 May, 11.59pm Approach to assessment: For your written problem solving attempts, you will be marked according to selection of the appropriate technique or procedure, execution of the technique/procedure, completeness, correctness, as well as the communication of the mathematics. You need to demonstrate these to the marker through your written submission. While you are encouraged to help each other, your submission should be your own work. Examples of acceptable help include (but are not limited to) showing helping someone to do a similar question or pointing them in the direction of relevant learning resources. Examples of unacceptable help include (but are not limited to) showing someone your solutions to these problems, answering problems for someone else, and using someone else's attempts at these problems to answer them yourself. Formatting and how to submit: Your neat handwritten work should be scanned or photographed in a manner that produces a readable electronic form. This should then be combined into a single PDF file for submission. Ensure that you leave enough time to submit your work in the appropriate format. Submit your written work via the links available on the Assessment page of the unit Blackboard site. CRICOS No. 00213J MZB101 MZB101 - Modelling with introductory calculus Submission 4 (Due 11.59pm, Friday 5 May). Weighted: 15% Note that an rough approximation/expected length for this submission is around 3-6 A4 pages. 1. For each of the following functions, find the indicated derivative. (a) For y( x ) = 3x2 e x , find y0 ( x ). (b) For f (t) = sin(2x 3x2 ), find f 0 (t). (c) For y = 3x2 + 1, find d2 y . dx2 2. The waterslide at an amusement park is shaped like the curve y= 4 , x+1 for x = 0 m to x = 5 m. What is the angle (with the positive horizontal axis) of the slide when x = 3 m? 3. I have a rainwater tank in my backyard. I use the tank to store storm water for later use in keeping my lawn looking absolutely spectacularly green without wasting precious and expensive metered water, which I would have to pay for. My tank holds 7000 L and can be completely drained in emergencies in just 90 minutes. In fact, when draining, the volume, V (in L), of water in the tank after t minutes of draining is given by the function 90 t 2 V = 7000 . 90 What is the instantaneous rate of draining after 10 minutes of the draining cycle? 4. The length of a pendulum is decreasing at a rate of 0.100 cm/s. What is the time rate of change of the period T (in sec) of the pendulum when L = 16.0 cm, if the equation relating the period and length is r L T=p ? 245 5. When real numbers are larger than 1, they are smaller than their own squared value. However, for real numbers between 0 and 1, this is not the case - they are larger than their own square. Use calculus to show that 0.5 is the positive real number that exceeds its own squared value by the greatest amount. Make sure to fully justify and communicate your answer. CRICOS No. 00213J MZB101