Higher Engineering Mathematics, Sixth Edition

Revision Test 3

This Revision Test covers the material contained in Chapters 8 to 10.The marks for each question are shown in
brackets at the end of each question.

1. Use Maclaurin’s series to determine a power series
   for e^2 xcos3xas far as the term inx^2 .(9)


2. Show, using Maclaurin’s series, that the first four
   terms of the power series for cosh 2xis given by:

cosh 2x= 1 + 2 x^2 +

2

3

x^4 +

4

45

x^6. (10)

3. Expand the function x^2 ln( 1 +sinx) using
   Maclaurin’s series and hence evaluate:
   ∫ 1
   2
   0

x^2 ln( 1 +sinx)dxcorrect to 2 significant

figures. (13)

4. Use the method of bisection to evaluate the root
   of the equation:x^3 + 5 x=11 in the rangex=1to
   x=2, correct to 3 significant figures. (11)


5. Repeat question 4 using an algebraic method of
   successive approximations. (16)


6. The solution to a differential equation associated
   with the path taken by a projectile for which the
   resistance to motion is proportional to the velocity
   is given by:

y= 2. 5 (ex−e−x)+x− 25

Use Newton’s method to determine the value ofx,

correct to 2 decimal places, for which the value of

yis zero. (10)

7. Convert the following binary numbers to decimal
   form:
   (a) 1101 (b) 101101.0101 (5)


8. Convert the following decimal number to binary
   form:
   (a) 27 (b) 44.1875 (9)


9. Convert the following decimal numbers to binary,
   via octal:
   (a) 479 (b) 185.2890625 (9)


10. Convert
    (a) 5F 16 into its decimal equivalent

(b) 132 10 into its hexadecimal equivalent

(c) 110101011 2 into its hexadecimal equivalent

(8)