CALCULUS III
FINAL EXAM
Sample 4
Student Name: ___________________________________________
Student ID Number: ______________________________________
Course Title: Calculus III
Duration of Exam: 2 Hours
Number of Exam Pages: 7 pages (including this cover sheet)
Exam Type: Closed book
Total Mark: /35
,Question 1 (5 marks)
𝜕𝑧
Find the value of at the point (1,1,1) if the equation
𝜕𝑥
𝑥𝑦 + 𝑧 3 𝑥 − 2𝑦𝑧 = 0
defines 𝑧 as a function of the two independent variables 𝑥 and 𝑦 and the partial derivative exist.
, Question 2 (5 marks)
𝜕𝑧 𝜕𝑧
Draw a dependency (branch) diagram and write a Chain Rule formula for and for
𝜕𝑡 𝜕𝑠
𝑧 = 𝑓(𝑥, 𝑦), 𝑥 = 𝑔(𝑡, 𝑠), 𝑦 = ℎ(𝑡, 𝑠)
FINAL EXAM
Sample 4
Student Name: ___________________________________________
Student ID Number: ______________________________________
Course Title: Calculus III
Duration of Exam: 2 Hours
Number of Exam Pages: 7 pages (including this cover sheet)
Exam Type: Closed book
Total Mark: /35
,Question 1 (5 marks)
𝜕𝑧
Find the value of at the point (1,1,1) if the equation
𝜕𝑥
𝑥𝑦 + 𝑧 3 𝑥 − 2𝑦𝑧 = 0
defines 𝑧 as a function of the two independent variables 𝑥 and 𝑦 and the partial derivative exist.
, Question 2 (5 marks)
𝜕𝑧 𝜕𝑧
Draw a dependency (branch) diagram and write a Chain Rule formula for and for
𝜕𝑡 𝜕𝑠
𝑧 = 𝑓(𝑥, 𝑦), 𝑥 = 𝑔(𝑡, 𝑠), 𝑦 = ℎ(𝑡, 𝑠)
