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Graphing Limits Calculus

Introduction to Graphing limits calculus:

Calculus is the branch of mathematics involving functions,derivatives,limits,infinite series and integrals. In this article we shall discuss about the graphing limits calculus with examples. We can classify calculus into differential calculus and integral calculus. Moreover we can define calculus as the study of change. The limits is the value of  a function at a point(input) with respect to it's nearby points(input).  The following are the examples explaining the graphing limits calculus.


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Graphing Limits Calculus Problems:


Example 1:

`lim_(x->2)(x+5)/(x+2)`

Solution: Here the function f(x) = (x + 5)  have the following conditions,              
                                                  (x + 2)

At point zero, we can say that numerator = 0

So, x+5 = 0 => x="-5.

At vertical asymptote at x="-2," since denominator = 0

x+2 = 0 => x="-2

At y-intercept, the function of x equal zero, then

f(x) = 0,  (0 + 5)  = 5
              (0 + 2)     2 

Divisionofx+5/x+2

Graphing (x + 5)
               (x + 2)

Graphinglimitsfor(x+5)/(x+2)

 

Example 2:

`lim_(x->oo)(100)/(x^2 + 5)`

`Solution: ``lim_(x->oo)(100)/(x^2 + 5)`

                    => 100
                      `oo`

Since 100 is a number, were the denominator x2 + 5  approaches `oo` as x extends to `oo`

so `lim_(x->oo)(100)/(x^2+5) = 0`

 

Example 3:

`lim_(x->oo)(7)/(x^3+100)`

`Solution:`

`lim_(x->oo)(7)/(x^3 + 100)`

                    => 7
                     `oo`

Since 7 is a number, were the denominator x3 + 100  approaches `oo` as x extends to `oo`

so `lim_(x->oo)(7)/(x^3+100) = 0`

 

Example 4:

`lim_(x->oo)(89)/(x^9+10)`

Solution:

 `lim_(x->oo)(89)/(x^9 + 10)`

                    =>89
                    `oo`

Since 89 is a number, were the denominator x9 + 10  approaches `oo` as x extends to `oo`

so `lim_(x->oo)(7)/(x^9+10) = 0`


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Graphing Limits Calculus Practice Problems:


Problem 1:Graph the given function `lim_(x->2)(x+6)/(x+3)`

Solution: 

Graphinglimitsfor(x+6)/(x+3)

 

 

 

 

 

 

 

 

 

 

 

 

 

Problem 2: Solve `lim_(x->oo)(10)/(x^3 + 9) `  

Solution: The given function is equal to zero.