chapter :02 title: limits and continuity
TRANSCRIPT
AVERAGE RATE OF CHANGE OR SECANT SLOP:
A line joining two point of a curve is a secant to the curve
Formula:
Example
1. παΊπ₯α» = π₯3 + 1, [2,3] 2. παΊπ₯α» = π₯3 + 1, [β1 , 1]
Chapter :02
Title: LIMITS AND CONTINUITY
ONE SIDED LIMIT:
RIGHT HAND LIMIT:
A function f is said to have the right-hand limit π as π₯ β π+
LEFT HAND LIMIT:
A function f is said to have the right-hand limit π as π₯ β πβ
If
The relationship between one-sided and two-sided limits
Example:
1. limπ₯β2
4 =
2. limπ₯ββ13
4 =
3. limπ₯β3
π₯ =
4. limπ₯β2
αΊ5π₯ β 3α» =
5. limπ₯ββ2
3π₯+4
π₯+5=
LIMITS LAW:
1. Identity function:
If f is the identity function παΊπ₯α» = π₯, then the limit at point π₯ = π₯0
2. Constant function:
If f is the constant function παΊπ₯α» = π, then the limit at point π₯ = π₯0
3. Sum Rule:
If limπ₯βπ
παΊπ₯α» = πΏ & limπ₯βπ
παΊπ₯α» = π then
4. Difference Rule:
If limπ₯βπ
παΊπ₯α» = πΏ & limπ₯βπ
παΊπ₯α» = π then
5. Constant Multiple Rule:
If limπ₯βπ
παΊπ₯α» = πΏ then
6. Quotient Rule:
If limπ₯βπ
παΊπ₯α» = πΏ & limπ₯βπ
παΊπ₯α» = π then
7. Power rule
If limπ₯βπ
παΊπ₯α» = πΏ then
Example: