Everything Maths Grade 12

6.4 CHAPTER 6. FUNCTIONS AND GRAPHS 1 2 3 − 1 − 2 − 3 3 2 − − 1 − 1 2 3 f (x) = x^2 f−^1 (x) = √ x f−^1 (x) =− √ x Figure 6.3: T ...

CHAPTER 6. FUNCTIONS AND GRAPHS 6.4 f (x) = 2x^2. (a) Draw the graph of f and state its domain and range. (b) Find f−^1 and, i ...

6.4 CHAPTER 6. FUNCTIONS AND GRAPHS 1 2 3 − 1 − 2 − 3 3 2 − − 1 − 1 2 3 f (x) = 10x f−^1 (x) = log(x) Figure 6.4: The function f ...

CHAPTER 6. FUNCTIONS AND GRAPHS 6.4 More practice video solutions or help at http://www.everythingmaths.co.za (1.) 01f8 (2.) 01f ...

6.4 CHAPTER 6. FUNCTIONS AND GRAPHS (b) Find the equation ofthe inverse of the abovegraph in the form y = ... (c) Now, sketch y ...

Differential Calculus 7 7.1 Introduction EMCBA Calculus is one of the central branches of mathematics and was developedfrom alge ...

7.2 CHAPTER 7. DIFFERENTIAL CALCULUS xA = xt (7.3) vAt = 1000 +vtt (7.4) (2 m· s−^1 )t = 1000 m + (0,25 m· s−^1 )t (7.5) (2 m· s ...

CHAPTER 7. DIFFERENTIAL CALCULUS 7.2 where a 1 is the first term of the series and r is the common ratio. We see that there are ...

7.2 CHAPTER 7. DIFFERENTIAL CALCULUS 8 6 − 4 − − 2 − 2 4 2 4 − 2 − 4 − 6 − 8 x y �� Figure 7.1: Graph of y =(x+6)(x+6x−2). Limit ...

CHAPTER 7. DIFFERENTIAL CALCULUS 7.2 Activity: Limits If f (x) = x + 1, determine: f (− 0 .1) f (− 0 .05) f (− 0 .04) f (− 0 .03 ...

7.2 CHAPTER 7. DIFFERENTIAL CALCULUS x y 7 − 5 − − 3 − (^11357) 1 3 − 1 − 3 Figure 7.2: Graph of y =^1 x. As x→ 0 from the left, ...

CHAPTER 7. DIFFERENTIAL CALCULUS 7.2 SOLUTION Step 1 : Simplify the expression There is nothing to simplify. Step 2 : Cancel all ...

7.2 CHAPTER 7. DIFFERENTIAL CALCULUS Example 4: Limits QUESTION Determine lim x→ 10 x^2 − 100 x− 10 SOLUTION Step 1 : Simplify t ...

CHAPTER 7. DIFFERENTIAL CALCULUS 7.2 We know how to calculate the average gradient between two points on a curve, but we needtwo ...

7.2 CHAPTER 7. DIFFERENTIAL CALCULUS point x = 2. SOLUTION Step 1 : Calculating the gradient at a point We know that the gradien ...

CHAPTER 7. DIFFERENTIAL CALCULUS 7.2 point x = a. SOLUTION Step 1 : Calculating the gradient at a point We know that the gradien ...

7.3 CHAPTER 7. DIFFERENTIAL CALCULUS 3. lim x→ 2 3 x^2 − 4 x 3 −x 4. lim x→ 4 x^2 −x− 12 x− 4 5. lim x→ 2 3 x + 1 3 x More pract ...

CHAPTER 7. DIFFERENTIAL CALCULUS 7.3 Example 7: Derivatives - First Principles QUESTION Calculate the derivativeof g(x) = x− 1 f ...

7.4 CHAPTER 7. DIFFERENTIAL CALCULUS Determine the derivative of f (x) = 1 x− 2 using first principles. Determine f�(3) from ...

CHAPTER 7. DIFFERENTIAL CALCULUS 7.4 Example 8: Rules of Differentiation QUESTION Determine the derivative of x− 1 using the rul ...