Basic Engineering Mathematics, Fifth Edition

308 Basic Engineering Mathematics (b) fails due to excessive vibration or excessive humidity, (c) will not fail because of both ...

Probability 309 Determine the probability that the total score is 8 when two like dice are thrown. The probability of eventAhap ...

310 Basic Engineering Mathematics Problem 8. A box contains 74 brass washers, 86 steel washers and 40 aluminium washers. Three w ...

Probability 311 Now try the following Practice Exercise PracticeExercise 130 Laws of probability (answers on page 354) The prob ...

Revision Test 13 : Statistics and probability This assignment covers the material contained in Chapters 31–33.The marks availabl ...

Chapter 34 Introduction to differentiation 34.1 Introduction to calculus Calculusis a branch of mathematics involving or lead- i ...

314 Basic Engineering Mathematics Givenf(x)= 3 x^3 + 2 x^2 − 3 x+2, prove that f( 1 )= 1 7 f( 2 ). 34.3 The gradient of a curv ...

Introduction to differentiation 315 chordJK.BymovingJnearer and nearer to K, determine the gradient of the tangent of the curve ...

316 Basic Engineering Mathematics When differentiating, results can be expressed in a number of ways. For example, (a) ify= 3 x^ ...

Introduction to differentiation 317 i.e. dy dx = 8 3 x^3 + 12 x^4 Problem 10. Iff(t)= 4 t+ 1 √ t^3 findf′(t) f(t)= 4 t+ 1 √ t^3 ...

318 Basic Engineering Mathematics y= 1 x y= 12 y=x− 1 x^2 y= 3 x^5 − 2 x^4 + 5 x^3 +x^2 − 1 y= 2 x^3 y= 4 x( 1 −x) y= √ ...

Introduction to differentiation 319 y (a) 0 (b) 0 y 5 cos x x radians x radians 1 2 2  2 1 dydx  3  2  2  2  3  2  2 dxd ...

320 Basic Engineering Mathematics Now try the following Practice Exercise PracticeExercise 134 Differentiation of sine and cosin ...

Introduction to differentiation 321 1.0 0.5 0123 (b) (a) y 5 In x 456 x 1.5 2 y 0 21 22 1 2 123456 x dy dx^5 1 x dy dx Figure 34 ...

322 Basic Engineering Mathematics dy dx = 3 (− 2 x−^3 )− 2 (4cos4x)+ 2 (−e−x)+ 1 x =− 6 x^3 −8cos4x− 2 ex + 1 x Now try the foll ...

Introduction to differentiation 323 34.10 Rates of change If a quantityydepends on and varies with a quantity xthen the rate of ...

324 Basic Engineering Mathematics Now try the following Practice Exercise PracticeExercise 138 Ratesof change (answers on page 3 ...

Chapter 35 Introduction to integration 35.1 The process of integration The process of integration reverses the process of differ ...

326 Basic Engineering Mathematics (b) When a sum of several terms is integrated the result is the sum of the integrals of the se ...

Introduction to integration 327 subtraction.) Hence, ∫( 3 + 2 5 x− 6 x^2 ) dx = 3 x+ ( 2 5 ) x^1 +^1 1 + 1 −( 6 ) x^2 +^1 2 + 1 ...