Cambridge Additional Mathematics

Introduction to differential calculus (Chapter 13) 361 3 Use the laws of logarithms to help differentiate with respect tox: a y= ...

362 Introduction to differential calculus (Chapter 13) THE DERIVATIVE OF tanx Consider y= tanx= sinx cosx We let u= sinx and v= ...

Introduction to differential calculus (Chapter 13) 363 EXERCISE 13K 1 Find dy dx for: a y= sin(2x) b y= sinx+ cosx c y= cos(3x)¡ ...

364 Introduction to differential calculus (Chapter 13) EXERCISE 13L 1 Find f^00 (x) given that: a f(x)=3x^2 ¡ 6 x+2 b f(x)= 2 p ...

Introduction to differential calculus (Chapter 13) 365 Review set 13A #endboxedheading 1 Evaluate: a lim x! 1 (6x¡7) b lim h! 0 ...

366 Introduction to differential calculus (Chapter 13) Review set 13B 1 Evaluate the limits: a lim h! 0 h^3 ¡ 3 h h b lim x! 1 3 ...

14 Applications of differential calculus Contents: A Tangents and normals B Stationary points C Kinematics D Rates of change E O ...

368 Applications of differential calculus (Chapter 14) Opening problem Michael rides up a hill and down the other side to his fr ...

A,(a¡f(a)) x=a y = f(x) point of contact tangent gradientmT normal (1 2), y x f(x) = x + 1 2 1 O point of inflection Application ...

(4 4), y x normal tangent gradientmN gradientmT O 370 Applications of differential calculus (Chapter 14) NORMALS Anormalto a cur ...

Applications of differential calculus (Chapter 14) 371 Example 3 Self Tutor Find the equations of any horizontal tangents to y=x ...

1 y x y= xln¡ O &__Q.,-1* 372 Applications of differential calculus (Chapter 14) Example 4 Self Tutor Show that the equation ...

(a a ), 2 y x y=x 2 (2 3), O (1) =1 x x must be a factor since we have the tangent at. ¡ 2 Applications of differential calculus ...

If two curves then they share a common tangent at that point. touch y x y=lnx y=ax 2 O^1 b 374 Applications of differential calc ...

y O x f(x) = x 3 y x D,(6 18) A,(-5 -16_ )Qw_ B,(-2 4) C,(2 -4) 2 -2 y = f(x) O Applications of differential calculus (Chapter 1 ...

-1 + - + 3 x f (x)' Stationary point where f^0 (a)=0 Sign diagram of f^0 (x) near x=a Shape of curve near x=a local maximum loca ...

We need to include points where is undefined as critical values of the sign diagram. fx() y O x 5 (-1 10), (3 -22), y=x -3x -9x+ ...

GRAPHING PACKAGE y y = f(x) x B A,(-2 8) C,(3 -11) -4 5 O 378 Applications of differential calculus (Chapter 14) Example 10 Self ...

If the domain is restricted, we need to check the value of the function at the endpoints of the domain. Applications of differen ...

DEMO OP origin s(t) 0 5 10 15 20 25 t=0 t=1 t=2 t=3 t=4 GRAPHING PACKAGE 380 Applications of differential calculus (Chapter 14) ...