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2014-2-SGOR-STARklang_MATHS QA by TAN LING LING

Section A [45 marks]

Answer all questions in this section.

1. (a) The function f is defined by

65

1)(

2

2

xx

xxf

.1,

1,

x

x Determine whether f

is continuous at 1x . [3 marks]

(b) Evaluate 1

45lim

1 x

xx

x. [3 marks]

2. Oil is poured into a hemispherical bowl of radius 5 cm at the rate of 4 cm3 s

1. The

volume of the oil in the bowl is given by when its depth is h cm. Given that at a

particular instant the depth of the oil is 2 cm. Find

(a) the rate of change of h, [3 marks]

(b) the rate of change of the radius of the surface area of the oil. [4 marks]

3. Find the exact value of dx, given your final answer in its simplest form.

[5 marks]

4. Find the solution of the differential equation ,

given that when . [10 marks]

5. Given that .

(a) Show that . [3 marks]

(b) in

ascending powers of x up to and including the term in . [6 marks]

(c) Given that the value of y, correct to 8 decimal places is 1.223 048 88 when

. Find the percentage error of the estimate. [3 marks]