Higher Engineering Mathematics, Sixth Edition
82 Higher Engineering Mathematics nearer to the required root. The procedure is repeated until the value of the required root do ...
Solving equations by iterative methods 83 Neglecting terms containing products ofδ 3 gives: 2. 3759 − 6. 1656 δ 3 + 4. 6242 − 6 ...
84 Higher Engineering Mathematics δ 2 ≈ − 11. 217 + 24. 090 − 6. 2084 − 7 21. 681 − 31. 042 + 4 ≈ − 0. 3354 − 5. 361 ≈ 0. 06256 ...
Solving equations by iterative methods 85 By Newton’s formula, a better approximation to the root is: r 2 = 1 − − 1 21 = 1 −(− 0 ...
86 Higher Engineering Mathematics f( 1 )= 53 −e^1.^92 +5cos 1 3 − 9 ≈ 114 f( 2 )= 63 −e^3.^84 +5cos 2 3 − 9 ≈ 164 f( 3 )= 73 −e^ ...
Chapter 10 Binary, octal and hexadecimal 10.1 Introduction All data in modern computers is stored as series ofbits, abitbeingabi ...
88 Higher Engineering Mathematics = 1 2 + 1 8 + 1 16 = 0. 5 + 0. 125 + 0. 0625 =0.6875 10 Problem 3. Convert 101.0101 2 to a dec ...
Binary, octal and hexadecimal 89 Problem 5. Convert 0.40625 10 to a binary number. From above, repeatedly multiplying by 2 gives ...
90 Higher Engineering Mathematics Problem 8. Perform the binary addition: 11111 + 10101 11111 + 10101 sum 110100 carry 11111 Pro ...
Binary, octal and hexadecimal 91 Table 10.1 Octal digit Natural binary number 0 000 1 001 2 010 3 011 4 100 5 101 6 110 7 111 Th ...
92 Higher Engineering Mathematics Using Table 10.1 to convert this binary number to an octal number gives 363. 428 and 363. (^42 ...
Binary, octal and hexadecimal 93 Table 10.2 Decimal Binary Octal Hexadecimal 0 0000 0 0 1 0001 1 1 2 0010 2 2 3 0011 3 3 4 0100 ...
94 Higher Engineering Mathematics Problem 18. Convert the following decimal numbers into their hexadecimal equivalents: (a) 37 1 ...
Binary, octal and hexadecimal 95 symbols to each group gives as above from Table 10.2. Thus, 1100111102 =19E 16 (d) Converting f ...
Revision Test 3 This Revision Test covers the material contained in Chapters 8 to 10.The marks for each question are shown in br ...
Chapter 11 Introduction to trigonometry 11.1 Trigonometry Trigonometryisthebranchofmathematicswhichdeals with the measurement of ...
98 Higher Engineering Mathematics Now try the following exercise Exercise 44 Further problems on the theorem of Pythagoras In a ...
Introduction to trigonometry 99 (vi) cotangentθ= adjacent side opposite side i.e. cotθ= a b c b a Figure 11.6 (b) From above, ...
100 Higher Engineering Mathematics B A 0 2 4 (a) (b) 68 8 f(x) 7 6 4 3 2 B A C 0 2 468 8 f(x) 6 4 2 Figure 11.8 Now try the foll ...
Introduction to trigonometry 101 values, correct to 4 decimal places, may be checked: secant 32◦= 1 cos32◦ = 1. 1792 cosecant 75 ...
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