# Limit, Continuity & Differentiability-IB Maths Topics

**Limit of a function**

**Limit of a function f(x) is said to exist as, ** **when**

**finite quantity.**

**Fundamental Theorems On Limits :**

Let & If *l* & m exists then :

(i) f (x) ± g (x) = l ± m

(ii) f(x). g(x) = l. m

(iii) provided

(iv) where k is a constant.

(v) provided f is continuous at g (x) = m

**Standard Limits** :

(a) and Where x is measured in radians

(b) both are equal to e

(c) then this will show that

(d) and (a finite quantity) then

where z=

(e) where a>0. In particular

**Indeterminant Forms**:

etc are considered to be indeterminant values

We cannot plot on the paper. Infinityis a symbol & not a number. It does not obey the laws of elementary algebra.

+=

×=

(a/) = 0 if a is finite v is not defined

a b =0,if & only if a = 0 or b = 0 and a & b are finite.

Expansion of function like Binomial expansion, exponential & logarithmic expansion, expansion of sinx , cosx , tanx should be remembered by heart & are given below:

**(i)** ** e ^{x} =1+x/1!+x^{3}/3!+x^{4}/4!……**

**(ii) a ^{x}=1+(xloga)/1!+ (xloga)^{2}/2!+ (xloga)^{3}/3!+ (xloga)^{4}/4!+……….**where a > 0

**(iii) ln(1-x)=x-x ^{2}/2+x^{3}/3-x^{4}/4………. where -1 < x 1**

**(iv) ln(1-x)=-x-x ^{2}/2-x^{3}/3-x^{4}/4………. where -1 x < 1**

**(v ) **

**(vi) **

**(v)**

In next post, I will discuss various types of limit problems, their solutions and L’ Hospital’s rule.In the meantime, you can solve these basic questions from this PDF. This PDF is for beginners only. I will post difficult and higher level questions in the next post on this topic