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Limit of Indeterminate Form and Algebraic limit is considered one the most difficult concept.
94 Questions around this concept.
Let be a positive increasing function with
Find limit
Find Limit :
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Find limit:
The value of is:
Find :
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The value of is
Is the function defined for all values of x ? Indicate the values of x for which it is defined and real. Find the limit as
Evaluate
Limit of Indeterminate Form and Algebraic limit
If we directly substitute x = a in f(x) while evaluating , and will get one of the seven following forms
then it is called indeterminate form.
For example,
Note:
1. form means the numerator and denominator are both tending to 0 (AND NOT exactly 0)
Eg, , when we input the values of x close to 0(and x>0), then denominator is tending to 0, but numerator values are not tending to 0 BUT numerator is exactly 0. So this is not
form.
2. We can convert one indeterminate form into another and vice verse.
We will divide the problems of finding limits into five categories, which are
Limit of Algebraic function
Trigonometric Limit
Logarithmic limit
Exponential limit
Miscellaneous forms
One by one we will discuss all of these.
1. Limit of Algebraic function
(a) Direct Substitution Method
To find , directly substitute the value of the limit of the variable. (i.e. substitute x = a) in the expression f (x)
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