MATHEMATICS GRADE 12 DIFFERENTIAL CALCULUS PART 1
DIFFERENTIAL CALCULUS
LIMITS, FIRST PRINCIPALS, RULES OF DIFFERENTIATION
AND THE EQUATION OF A TANGENT TO A FUNCTION
1. LIMITS
When finding a limit, we look at what happens to a function value of a curve
(y – value) as we get closer and closer to a specific x – value on the curve.
When writing a limit, we use the notation lim f ( x)
xc
The abbreviation ‘lim’ tells us we are finding a limit
The notation ‘ ’ tells us which specific value the x – value is
approaching
represents the function with which we are working
Examples:
1
, MATHEMATICS GRADE 12 DIFFERENTIAL CALCULUS PART 1
The DERIVATIVE of a function gives the GRADIENT (or rate of change) of that
function at any point on the curve.
2. FIRST PRINCIPLES & THE RULES OF DIFFERENTIATION
2
DIFFERENTIAL CALCULUS
LIMITS, FIRST PRINCIPALS, RULES OF DIFFERENTIATION
AND THE EQUATION OF A TANGENT TO A FUNCTION
1. LIMITS
When finding a limit, we look at what happens to a function value of a curve
(y – value) as we get closer and closer to a specific x – value on the curve.
When writing a limit, we use the notation lim f ( x)
xc
The abbreviation ‘lim’ tells us we are finding a limit
The notation ‘ ’ tells us which specific value the x – value is
approaching
represents the function with which we are working
Examples:
1
, MATHEMATICS GRADE 12 DIFFERENTIAL CALCULUS PART 1
The DERIVATIVE of a function gives the GRADIENT (or rate of change) of that
function at any point on the curve.
2. FIRST PRINCIPLES & THE RULES OF DIFFERENTIATION
2
