Foundations of Engineering Calculus KXEX-1144

Faculty of Engineering, University of Malaya Group-01 & 02

Assignment No. 01, Marks - 10

1. Sketch the graph and hence find the domain and range of each of the following function: (2)

(i) ( )f x 4 x 2= − − (ii) x cos t, y sin t= =

2. Show that ( )2x 2; x 1

f xx 2; x 1⎧ + ≤

= ⎨+ >⎩

is continuous but not differentiable at x = 1.

Sketch the graph of f(x). (2)

3. Find the exact value of the given quantity without using calculator or tables (2)

(i) 1 3sec sin4

−⎡ ⎤⎛ ⎞−⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦

(ii) 1 3sin 2cos5

−⎡ ⎤⎛ ⎞⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦

4. If 16

12 +

=x

y find yn (2)

5. Find the dimensions of a rectangle with perimeter 100 ft whose area is as large as possible. (2)