Proof Of Limit As X Approaches C Of A Equals A

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					Proof Of Limit As X Approaches C Of A Equals A
Proof Of Limit As X Approaches C Of A Equals A

The following problems require the use of the algebraic computation of limits of functions as x
approaches a constant. Most problems are average. A few are somewhat challenging. All of
the solutions are given WITHOUT the use of L'Hopital's Rule.

If you are going to try these problems before looking at the solutions, you can avoid common
mistakes by giving careful consideration to the form during the computations of these limits.
Initially, many students INCORRECTLY conclude that is equal to 1 or 0 , or that the limit
does not exist or is or .

In fact, the form is an example of an indeterminate form. This simply means that you have
not yet determined an answer. Usually, this indeterminate form can be circumvented by using
algebraic manipulation.

Such tools as algebraic simplification, factoring, and conjugates can easily be used to
circumvent the form so that the limit can be calculated.

Before talking about limits in calculus, one must be familiar with few basic topics of calculus
like functions, range and domain.
                      Know More About Multiply And Divide Rational Numbers                                                    Page No. : ­ 1/4
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 function.

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.

2x2 will always tend towards infinity and -5x always tends towards minus infinity if, 'x' will
increase where will the function tends?

It will always depend on the value of if x2 will grow more rapidly with respect to x as x
increases then the function will surely tend towards the positive infinity

Now, let’s talk about the degree of the function, it can be defined as the highest power of
variable for example:

5x2 +6x+7,

In this x2 has highest power as two so degree of the function will be 2. The degree of the
function can be negative or positive. If degree of the function, is greater than 0 then, limit will
always be positive. If degree of the function is less than 0 then the limit will be 0.

                                      Read  More About Laplace Transform History                                                       Page No. : ­ 2/4
lim x→c kf(x) = k. lim x→c f(x) =kL
lim x→c [f(x) +g(x)] = lim x→c f(x) + lim x→c g(x) =L+M
lim x→c [f(x) -g(x)] = lim x→c f(x) - lim x→c g(x) =L-M
lim x→c [f(x)g(x)] = lim x→c f(x) lim x→c g(x) =LM

Example: Solve the limit function where,
lim x→2 x3 + x2 +1?

Solution: For solving this limit function we have to follow the expression given below.
Step 1: In first step we write the given limit function,

lim x→2 x3 + x2 +1,

Step 2 : In second step we have solved particular values,

lim x→2 x3 + lim x→2 x2 +lim x→2 1,
lim x→2(2)3 + lim x→2 (2)2 +1,
8 + 4 +1 = 13,

Now we get the value of limit of function is 13.                                                      Page No. : ­ 3/4
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