MTH109 Tutor-Marked Assignment 1 This project is price 10% of the final effect for MTH109 Calculus. The decrease-off date for this project is 05 March 2026, 2355hrs. Sing to Students: It’s most likely you’ll perchance also very properly be to contain the following particulars for your submission: Course Code, Title of the TMA, SUSS PI No., Your Establish, and Submission Date. As an illustration, ABC123 TMA01 Sally001 TanMeiMeiSally (leave out D/O, S/O). Exhaust underscore and no longer home. Demand 1 Resolve the following limits. Demand 2 The Air Quality Health Index (AQHI) is a scale from 1 to 11 that is venerable to discuss the stage of properly being possibility linked with air quality. A sample of 647 readings of air air pollution taken at a monitoring speak over a effect duration is venerable to calculate 647 values of the AQHI. Desk Q2 presentations the frequency counts of every price of the AQHI essentially based completely completely on these readings. Given a sample X 1 ,…,Xn of n observations of the AQHI, the (uncorrected) sample variance s 2(µ) relative to a parameter µ is given by n s 2(µ) = 1n i∑=1(Xi −µ)2 . AQHI 1 2 3 4 5 6 7 8 9 10 11 Frequency 0 38 197 206 152 47 7 0 0 0 0 Desk Q2: Frequency counts of AQHI values. (a) Put together spinoff exams by differentiating with appreciate to µ to point to that s 2(µ) is minimised when 1 n µ = X = n i∑=1Xi , the sample mean. (10 marks) (b) Calculate the discover of the sample variance s 2(X) for the AQHI data in Desk Q2, giving your reply honest to 2 decimal locations. (5 marks) Demand 3 (a) Outline a aim f : R −→ R by the establish a and b are genuine constants. (i) Resolve the variety of values of a and b such that f is continuous at x= (5 marks) (ii) The exhaust of the restrict definition of differentiability, resolve the variety of values of a and b such that f is differentiable at x = (10 marks) (b) A rectangular sheet of paper OACB is folded over so that the nook O correct reaches a point P on the side AC as proven in Resolve Q3b. Let OA = a and OB = b, the establish 0 < a < b, and let x = AP. As P strikes from A to C, the sq. of the length of the crease shaped by the fold is given by the aim L 2(x) : [0,b] −→ R defined by (i) Resolve whether the aim L 2(x) is continuous over [0,b]. (5 marks) (ii) Resolve the variety of values of a and b, self-discipline to 0 < a < b < ∞, such that the aim√ L 2(x) has a unusual most over [0,b] at x = b− b 2 −a 2. (10 marks) Demand 4 (a) Demonstrate that the tangent line to the graph of the equation y 2 =x 3 on the purpose 8/9, 16√2/27 is additionally a popular to the graph one day. (5 marks) (b) Demonstrate that the tangent traces to the graph of the equation y 2(x−1) = x 2(x+1) on the components the establish x = 2 intersect at an attitude of . (3 marks) Demand 5 END OF ASSIGNMENT
- WE OFFER THE BEST CUSTOM PAPER WRITING SERVICES. WE HAVE DONE THIS QUESTION BEFORE, WE CAN ALSO DO IT FOR YOU.
- Assignment status: Already Solved By Our Experts
- (USA, AUS, UK & CA PhD. Writers)
- CLICK HERE TO GET A PROFESSIONAL WRITER TO WORK ON THIS PAPER AND OTHER SIMILAR PAPERS, GET A NON PLAGIARIZED PAPER FROM OUR EXPERTS
QUALITY: 100% ORIGINAL PAPER – NO ChatGPT.NO PLAGIARISM – CUSTOM PAPER
Looking for unparalleled custom paper writing services? Our team of experienced professionals at AcademicWritersBay.com is here to provide you with top-notch assistance that caters to your unique needs.
We understand the importance of producing original, high-quality papers that reflect your personal voice and meet the rigorous standards of academia. That’s why we assure you that our work is completely plagiarism-free—we craft bespoke solutions tailored exclusively for you.
Why Choose AcademicWritersBay.com?
- Our papers are 100% original, custom-written from scratch.
- We’re here to support you around the clock, any day of the year.
- You’ll find our prices competitive and reasonable.
- We handle papers across all subjects, regardless of urgency or difficulty.
- Need a paper urgently? We can deliver within 6 hours!
- Relax with our on-time delivery commitment.
- We offer money-back and privacy guarantees to ensure your satisfaction and confidentiality.
- Benefit from unlimited amendments upon request to get the paper you envisioned.
- We pledge our dedication to meeting your expectations and achieving the grade you deserve.
Our Process: Getting started with us is as simple as can be. Here’s how to do it:
- Click on the “Place Your Order” tab at the top or the “Order Now” button at the bottom. You’ll be directed to our order form.
- Provide the specifics of your paper in the “PAPER DETAILS” section.
- Select your academic level, the deadline, and the required number of pages.
- Click on “CREATE ACCOUNT & SIGN IN” to provide your registration details, then “PROCEED TO CHECKOUT.”
- Follow the simple payment instructions and soon, our writers will be hard at work on your paper.
AcademicWritersBay.com is dedicated to expediting the writing process without compromising on quality. Our roster of writers boasts individuals with advanced degrees—Masters and PhDs—in a myriad of disciplines, ensuring that no matter the complexity or field of your assignment, we have the expertise to tackle it with finesse. Our quick turnover doesn’t mean rushed work; it means efficiency and priority handling, ensuring your deadlines are met with the excellence your academics demand.
