Compute the value of the following limit, Mathematics

Compute the value of the following limit.

2099_limit2.png

Solution: Notice as well that I did say estimate the value of the limit.  Again, we will not directly compute limits in this section. The point of this section is to give us a better idea of how limits work & what they can tell us regarding the function.

We will select values of x that get closer and closer to x=2 & plug these values into the function.  Doing this gives the following table of values.

712_limit3.png

Note that we ensured & picked values of x that were on both sides of x = 2 to ensure that any trends which we might be seeing are x =2 and which we moved in extremely close to actually correct.

Also notice as well that we can't in fact plug in x = 2 into the function as it would give us a division by zero error.  It is not a problem as the limit doesn't care what is happening at the point in question.

From given table it appears that the function is 4 as x approaches 2, so

132_limit4.png

Let's think a little bit more about what's going on here.  Let's graph the function from the last example.  The graph of the function in the range of x's that were interested in is shown below.

883_limit5.png

Posted Date: 4/11/2013 4:02:07 AM | Location : United States







Related Discussions:- Compute the value of the following limit, Assignment Help, Ask Question on Compute the value of the following limit, Get Answer, Expert's Help, Compute the value of the following limit Discussions

Write discussion on Compute the value of the following limit
Your posts are moderated
Related Questions
Mark is preparing a walkway around his inground pool. The pool is 20 by 40 ft and the walkway is intended to be 4 ft wide. Determine the area of the walkway? a. 224 ft 2 b.

Find out the roots of the following quadratic equation. 3x 2 + 7x = 0 Solution: Using Equation 6, one root is determined. x = 0 Using Equation 7, substitute the

Ten is decreased through four times the quantity of eight minus three. One is then added to in which result. What is the final answer? The area of a square whose side measures

Errors Are Useful :  While teaching children, you must have found theft making mistakes off and on. How do you respond to the errors'? What do they tell you about the child-failur

simplify the expression 3/5/64

Find the sum og series 1+(1+3)+(1+3+5)+.......+(1+3+...+15+17)=

Advantages and disadvantages of operation researchs

find the unit rate. Round to the nearest hundredth in necessary 325 meters in 28 seconds

A leap year has 366 days, therefore 52 weeks i.e. 52 Sunday and 2 days. The remaining 2 days may be any of the following : (i) Sunday and Monday (ii) Monday and Tuesday (iii)

Marty used the subsequent mathematical statement to show he could change an expression and still get the similar answer on both sides: 10 × (6 × 5) = (10 × 6) × 5 Which mathematica