Consider f (x) = (-7x^3 + 2)/(10x^3 + 3x + 2)

a) Construct a table of values to determing lim f(x) x to infinity

b) Use algebra to determin lim f(x)

x to infinity

c) Sketch the graph and indicate on the graph the behavior described by the limit.

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- Jul 27th 2006, 11:51 PMaskmemathLimits
Consider f (x) = (-7x^3 + 2)/(10x^3 + 3x + 2)

a) Construct a table of values to determing lim f(x) x to infinity

b) Use algebra to determin lim f(x)

x to infinity

c) Sketch the graph and indicate on the graph the behavior described by the limit. - Jul 28th 2006, 03:58 AMgalactus
part a. plug and chug.

For part b, get rid of everything but the highest powers in the num. and den.

You are left with:

Now, you can see what the limit is, can't you?.

part c. You have a graphing calculator?. - Jul 28th 2006, 07:06 AMThePerfectHacker
This is my 18:):)th Post!!!

- Jul 28th 2006, 08:50 AMaskmemathQuote:

Originally Posted by**galactus**

Can I plug in any value that I like? Arent I supposed to follow a sequence or something??

For part B how can I just get rid of everything but the highest powers?

L'Hospital Rule?? - Jul 28th 2006, 09:15 AMgalactus
Just plug in higher and higher values and watch it approach the limit.

See, it's approaching

Now, make it official with part b. Rational functions, especially with polynomials, are one of the easiest things in which to take a limit.

For part b, no, just erase them. In a rational function, if the limit approaches infinity, it is unaffected if you discard everything but the highest powers. Think about it. See?.

Suppose I had

If x gets huge, towards infinity, what are the 5 and 6 going to amount to?. Nothing. So, get rid of them and take the limit of 3x/6x. Which is 3/6=1/2.

Yours works the same.

- Jul 28th 2006, 09:31 AMThePerfectHackerQuote:

Originally Posted by**askmemath**

Divide numerator and denominator by ,

as,

Becuase,