ABSTRACT
U2 given that θ f = 3.5, θi = 2.5, R = 0.315, J = 0.4, U1 = 50 (6)
7. Solve, correct to 4 significant figures:
(a) 13e2x−1 = 7ex (b) ln(x + 1)2 = ln(x + 1)− ln(x + 2)+ 2
(15) 8. Determine the 20th term of the series 15.6, 15,
14.4, 13.8, . . . (3) 9. The sum of 13 terms of an arithmetic progression
is 286 and the common difference is 3. Determine the first term of the series (4)
10. Determine the 11th term of the series 1.5, 3, 6, 12, . . . (2)
11. A machine is to have seven speeds ranging from 25 rev/min to 500 rev/min. If the speeds form a geometric progression, determine their value, each correct to the nearest whole number (8)
12. Use the binomial series to expand (2a −3b)6 (7)
13. Expand the following in ascending powers of t as far as the term in t3
(a) 1 1+ t (b)
1√ 1−3t
For each case, state the limits for which the expansion is valid (9)
14. The modulus of rigidity G is given by G = R 4θ
L where R is the radius, θ the angle of twist and L the length. Find the approximate percentage error in G when R is measured 1.5% too large, θ is measure 3% too small and L is measured 1% too small (6)
15. 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 of x , correct to 2 decimal places, for which the value of y is zero (11)
For lecturers/instructors/teachers, fully worked solutions to each of the problems in Revision Test 4, together with a full marking scheme, are available at the website:
