# 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)  ex =1+x/1!+x3/3!+x4/4!……

(ii)  ax=1+(xloga)/1!+ (xloga)2/2!+ (xloga)3/3!+ (xloga)4/4!+……….where a > 0

(iii)   ln(1-x)=x-x2/2+x3/3-x4/4……….    where -1 < x  1

(iv)  ln(1-x)=-x-x2/2-x3/3-x4/4……….     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