Limits involving Binomial Expressions
» Special case of canceling factors in numerator and denominator
» With change of variable x=1+yx=1+y and constant a=1a=1
Factoring binomials refers to factoring of an-bnan−bn.
The word binomial means: of two terms.
The expression an-bnan−bn is a two variate binomial of degree n.
two variate : a and b are two variables
binomial : an and -bn are the two terms
degree n: The maximum power is n
Factoring the binomials is given by
The value of f(x)=x4-16x-2 at x=2 is 00 by direct substitution x=2.
The limit of f(x)=x4-16x-2 at x=2 is 4×23.
limit of f(x)=x4-16x-2 at x=2.
On substitution of x=2 the function evaluates to 00
Limit of the function is
note: (x-2) is not canceled at x=2. But, limit is applied to x-2x-2
To find limit of functions with binomials, factor the binomials to cancel out the factor involving 0.
What is the limit for f(x)=x15-1x10-1 at x=1
The answer is '32'
Limit of expressions with Binomials: For any positive integer n
The outline of material to learn "limits (calculus)" is as follows.
Note : click here for detailed outline of Limits(Calculus).
→ Indeterminate and Undefined
→ Indeterminate value in Functions
→ Expected Value
→ Definition by Limits
→ Geometrical Explanation for Limits
→ Limit with Numerator and Denominator
→ Limits of Ratios - Examples
→ L'hospital Rule
→ Examining a function
→ Algebra of Limits
→ Limit of a Polynomial
→ Limit of Ratio of Zeros
→ Limit of ratio of infinities
→ limit of Binomial
→ Limit of Non-algebraic Functions