How To Do Limits by tutorcircleteam


									                          How To Do Limits
How To Do Limits

In this article, our main focus is how to solve limits in calculus? But, before we move
to this question, let's have a look on Limits. Limits, are used to find the value of any
given function f(x) at a particular time when, x->a.

For Example, Solve f(x) = Lim (5-x) x-> 2 This means we need to find the value of a
given function at a particular value when x=2. If we put the value of x=2 in the above
function, we get: f(2) = (5-2), so, f(2) = 3.

In some cases, it becomes difficult for us to find the value of the given functions, i.e.
the value is not defined. To understand this let's take an example: f(x)= (x^2 -25) / (x-
5), x->5 Solve the problem by putting value of x=5, on doing so we get: f(5)= (5^5
-25)/ (5-5), = (25-25) /0, = 0/0.

Thus, we find this value is not possible. To solve such problems of limits, we first find
the factors of the functions, cancel the common numerator and denominator, and
then get the solution.
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In the above problem, lim f(x)= (x-5)(x+5) / (x-5) x->5 Cancelling x-5 from numerator
and denominator we get: f(x) =x+5 x->5 Putting x=5 in the above function we get: f(5)
= 5+5 f(5) =10.

Certain rules are to be followed to solve the functions of limits:
1. If a function is a simple function, f(x) at x=a, then simply put the value of x=a in the
function and solve it.

2. If the function f(x) is any rational number, then factorize the given function, find
what is common in numerator and denominator, cancel them and solve for the value
of x.

3. If the function is a surd, then to simplify for any value x=a, we first multiply the
numerator and denominator by its conjugate surd. Now, we simplify And find the
value of the function for x=a.

4. If the given function is a series, which can be expanded, then simply expand it,
simplify it and cancel common numerator and denominator then, substitute the value
of x=a to get the solution.

Before talking about limits in calculus, one must be familiar with few basic topics of
calculus like functions, range and domain. These are very important to understand
the concept of math because these are the basics requirement for studying calculus
limits. So in calculus you can say that a function’s behavior is called limit of that

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The definition of a limit is not concerned with value of f(x) when, x=c. So, we care
about the values of f(x) when x is close to c, on either the left side or right side.

Now, we move on to rules regarding limits. Limits have some rules which are useful
when we solve different limit problems.

First Rule: First rule is called as the constant rule. In this rule we state- if we have f(x)
=b (where f is constant for all x) then, the limits as x approaches c must be equal to b.                                                   Page No. : ­ 3/4
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