MTH316 Assignement 01: Multivariable Calculus -Singapore University of Social Sciences (SUSS)
University | SINGAPORE UNIVERSITY OF SOCIAL SCIENCES (SUSS) |
Subject | MTH316 Multivariable Calculus |
TUTOR-MARKED ASSIGNMENT 01 (TMA01)
This assignment is worth 12% of the final mark for MTH316 Multivariable Calculus.
The cut-off date for this assignment is 27 February 2025, 2355hrs.
Note to Students:
You are to include the following particulars in your submission: Course Code, Title of the
TMA, SUSS PI No., Your Name, and Submission Date.
For example, ABC123_TMA01_Sally001_TanMeiMeiSally (omit D/O, S/O). Use underscore
and not space.
Question 1
(a) Determine the value of k for the function π to be continuous at (0, 0), if any. (Use this value of k for the following sub-questions.) (10 marks)
(b) Show that ππ₯ (0, 0) and ππ¦ (0, 0) both exist and find their values. (10 marks)
(c) Define ππ₯ (π₯, π¦) and ππ¦ (π₯, π¦) each as a piecewise function in the entire domain of β2. (12 marks)
(d) Hence or otherwise, explain whether the function π is differentiable at (0,0).
(18 marks)
Question 2
A GPS application designed for hikers measures the altitude, z, at various positions on a terrain and performs a regression, yielding the altitude function below, where x, y and z are measured in km.
(a) State an equation that describes the level set of the function and use it to plot the contours of the terrain at the altitudes of 1.3 km, 1.5 km and 2 km with a graph plotter. Attach a screenshot of the graph and label each contour with its equation clearly. (8 marks)
(b) A hiker crosses the position (0, 1) while walking along a contour. Determine the contour equation and calculate the gradient vector of the terrain function at the position (0, 1). Show that this gradient vector is orthogonal to the contour at the position (0, 1). (18 marks)
(c) A hiker is walking along a path given by π¦ = 1 β π₯ β π₯ 3 . Sketch the path on your graph in part (a) and compute the directional derivative along the path at (0, 1) in the direction of increasing altitude. Explain briefly the meaning of this value of the directional derivative. (10 marks)
(d) The GPS carried by the hiker in part (c) shows that his ground speed is 0.8 m/s. Compute the rate of ascent (with respect to time) of the hiker as he crosses (0, 1). What is the degree of slope and how fast is he walking in the upslope direction? (7 marks)
(e) Another hiker is planning to walk from (5/2, 5/4) to (4, 2) in a straight line. From the contours plotted in part (a), explain the terrain he will experience along this path (without using calculations). (7 marks)
Hire a Professional Essay & Assignment Writer for completing your Academic Assessments
- Assignment: Shaping Personal Identity: The Impact of Gender and Ethnicity on Personal Identity
- Assignment: Production Plan Synopsis: Annie – A College Musical Experience in Singapore
- Assignment: Legal Strategies for Partnership Disputes: Priya’s Case in EcoJourney Pte Ltd
- ECE302 ECA: Understanding and Supporting Young Childrenβs Emotional Development
- PSY355 ECA: Psychology of Creativity: Creative Problem Solving in Organisations
- ST2195 Coursework Project: Programming for Data Science
- Assignment: Financial Statement Analysis of a Listed Company
- COM273 ECA: Creative Communication Strategies
- Teacher Portfolio: Reflections and Growth as an Early Childhood Educator
- NCO201 TMA02: Learn to Learn, Learn for Life Self-Directed Learning Plan and Reflection
UP TO 15 % DISCOUNT