Assignment
Instructions
- Please print the questions on A4 paper and write the answer in the box under each
question.
- Please scan your assignment as pdf le and upload the pdf le to Moodle according to
the order of the questions. No need to scan this page.
- Write in blue or black. Don’t use pencil for writing assignments.
- You should always give precise and adequate explanations to support your conclusions.
Clarity of presentation of your argument counts. So think carefully before you write.
- The submitted le over 30 Mb may not be displaced in the Moodle.
- Not properly scanned work (oversized, blurred, upside down) may not be graded.
- Late work will not be accepted.
- Full marks of this assignment is 2.
Questions 1 - 4 carry 0.3 point each and Questions 5 - 6 carries 0.4 point each.
Solution:
2. Three resistors of resistances R1, R2 and R3 connected in parallel produce a resistance R
given by 1R = 1R1 + 1R2 + 1R3 . Express R in terms of R1, R2 and R3. Compute @R@Rj for
3. Suppose g(u) is a C1-function of u and let w = pxy g
: Use the chain rule of
di erentiation to evaluate the expression x@w@x +y@w@y w.
Solution:
4. Use total di erential to approximate 3p4:982 + 1:052 + 0:962.
Solution:5. Let w = x2 +y2 z2, x = sin cos ; y = sin sin and z = cos . Calculate @w@ and
Solution:6. The length and width of a rectangle are measured with percentage errors of 0:5%. Ap-
proximate the maximun percentage error if total di ernetial is used in calculating the
length of the diagonal, s = px2 +y2 where x and y are the length and width respectively.
Solution: