NDA Math Limit, Continuity and Differentiability

Concept:
Continuity of a function:
- A function f(x) is said to be continuous at a point x=a in its domain, if

lim

x→a

f(x) exists or if its graph is a single unbroken curve at that point.
- f(x) is continuous at x=a⇔

lim

x→a+

f(x)=

lim

x→a−

f(x)=

lim

x→a

f(x)=f(a)
Calculation:

lim

x→2

‌

x3+x2

x2+3x+2

‌‌=‌

23+22

22+3⋅2+2

‌‌=‌

12

12

‌‌=1