Higher Engineering Mathematics, Sixth Edition
2 Higher Engineering Mathematics Problem 5. Simplify (x^2 √ y)( √ x^3 √ y^2 ) (x^5 y^3 ) 1 2 (x^2 √ y)( √ x^3 √ y^2 ) (x^5 y^3 ) ...
Algebra 3 3 c+ 2 c× 4 c+c÷ 5 c− 8 c = 3 c+ 2 c× 4 c+ (c 5 c ) − 8 c = 3 c+ 8 c^2 + 1 5 − 8 c = 8 c^2 − 5 c+ 1 5 or c(8c−5)+ 1 5 ...
4 Higher Engineering Mathematics √ t (√ t+ 3 √ t ) = 2 √ t i.e. √ t+ 3 = 2 √ t and 3 = 2 √ t− √ t i.e. 3 = √ t and 9 =t (b) Tran ...
Algebra 5 5 ×equation (1) gives: 35 x− 10 y= 130 (3) 2 ×equation (2) gives: 12 x+ 10 y= 58 (4) equation (3)+equation (4) gives: ...
6 Higher Engineering Mathematics Now try the following exercise Exercise 4 Further problems on simultaneous and quadratic equati ...
Algebra 7 Problem 23. Divide 2x^2 +x−3byx−1. 2 x^2 +x−3 is called thedividendandx−1thedivi- sor. The usual layout is shown below ...
8 Higher Engineering Mathematics The zero’s shown in the dividend are not normally shown,butareincludedtoclarifythesubtractionpr ...
Algebra 9 expressionx^2 + 2 x−8. We wouldn’t normally solve quadratic equations this way — but suppose we have to factorize a cu ...
10 Higher Engineering Mathematics x^2 − x − 6 ————————– x− 1 ) x^3 − 2 x^2 − 5 x+ 6 x^3 − x^2 − x^2 − 5 x+ 6 − x^2 + x ————– − 6 ...
Algebra 11 In this case the other factor is( 2 x+ 3 ), i.e., ( 2 x^2 +x− 3 )=(x− 1 )( 2 x− 3 ) Theremainder theoremmay also be s ...
12 Higher Engineering Mathematics ap^3 +bp^2 +cp+d,wherea=1, b=−2,c=−5,d=6andp=3. Hence the remainder is: 1 ( 3 )^3 +(− 2 )( 3 ) ...
Chapter 2 Partial fractions 2.1 Introduction to partial fractions By algebraic addition, 1 x− 2 + 3 x+ 1 = (x+ 1 )+ 3 (x− 2 ) (x ...
14 Higher Engineering Mathematics The denominator factorizes as (x−1) (x+3) and the numerator is of less degree than the denomin ...
Partial fractions 15 The denominatoris ofthe same degree as the numerator. Thus dividing out gives: 1 x^2 − 3 x+ 2 ) x^2 + 1 x^2 ...
16 Higher Engineering Mathematics 5. x^2 + 9 x+ 8 x^2 +x− 6 [ 1 + 2 (x+ 3 ) + 6 (x− 2 ) ] 6. x^2 −x− 14 x^2 − 2 x− 3 [ 1 − 2 (x− ...
Partial fractions 17 Equating thexterm coefficients gives: − 2 ≡− 2 A+ 2 B+C WhenA=2,B=3andC=−4then − 2 A+ 2 B+C=− 2 ( 2 )+ 2 ( ...
18 Higher Engineering Mathematics The denominator is a combination of a quadratic factor, (x^2 + 2 ), which does not factorize w ...
Partial fractions 19 x^3 + 4 x^2 + 20 x− 7 (x− 1 )^2 (x^2 + 8 ) [ 3 (x− 1 ) + 2 (x− 1 )^2 + 1 − 2 x (x^2 + 8 ) ] When solvi ...
Chapter 3 Logarithms 3.1 Introduction to logarithms With the use of calculators firmly established, logarith- mic tables are now ...
Logarithms 21 Problem 1. Evaluate log 3 9. Letx=log 3 9then3x= 9 from the definition of a logarithm, i.e. 3 x= 32 from which,x= ...
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