Limits Of Functions And Differentiation From The First Principle

Introduction to Limits

EVALUATION

Evaluate lim -> 4 x³ +4x 6 Evaluastelim x -> -2 x+6/ 2x +4

Differentiation From first Principle

EVALUATION

Find the derivative of the following using first principle. 1.   y=3x² + 4          (2) y= x³ -2x² + 2x -5

GENERAL EVALUATION

1. Evaluate  (i) lim x-> 0  x⁴  + 5x / x²  + 3   (ii) lim x-> 2    3x + 7
2. Differentiate from the first principle   y= 2x² +3x + 5
3. Find the gradient function of y = x² +3x +1 (4) Differentiate y =5x⁴ +7x³ + 6x² – 9x +4

READING ASSIGNMENT:New further Maths Project 2 page 113- 120

WEEKEND ASSIGNMENT

1. Evaluate limx-> 1 4x² + 3x a) 4 b) 3 c) 7 d) 0
2. Evaluate limx-> 0 x² + 9 a) 3 b) 9 c) 6 d) 1

3) Evaluate limx-> 0 ( x+3) ( 3x-3) a) 27 b) 6 c) 9 d) -9

• Differentiate 8x² + 10 a) 8x b) 16x c) 10 d) 18x
• Find the derivative of y = b where  b is a constant   a) 0 b) bx c) x d) 1

THEORY

1. Evaluate  limx-> -2       3x³ +4 / x² +4 (2) Differentiate from the first principle y = 7x³ + 5x² – 6x +5