finding limits of rational functions, piecewise functions

Hemant

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Apr 10, 2007
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1
Can someone please solve these questions step wise and give me the final answer. My maths is not that great and i am stuck up with my assignments

1. Find: lim [x->infty] (23x^3 + 45x) / (78x^3 + 9)

2. Determine whether f(x) is continuous at x = 5, for f(x) defined as follows:

. . .{ x, if x is an integer
. . .{ 10-x, if x is a real number which is not an integer
 
Hemant said:
Can someone please solve these questions step wise and give me the final answer.
There is a guy who surfs by here sometimes who will gladly provide you with the complete solution to hand in as your own work. But I'm afraid legitimate tutors don't do this. Instead, we try to help students learn how to do the material on their own. If you are indeed wanting somebody to complete your assignment for you, either wait and hope, or else pull out your mother's credit card, and pay one of the "services" which does this. (Many, probably most, of those sorts of places are dubious at best. Use the credit card with the lowest credit limit, to minimize potential damages.)

On the other hand, if you would like to do your work yourself, please reply showing what you have tried so far, and explaining where you are stuck. We'll be glad to provide hints, examples, links, and/or suggestions to help you get un-stuck.

For instance, for (1), if you're taking limits, then you've already taken algebra and worked with rational functions. So you already know about horizontal asymptotes. So where are you stuck?

For (2), you could at least look at the graph, couldn't you?

When you reply, please be complete and specific. Thank you.

Eliz.
 
For #2 answer these two questions.

\(\displaystyle \L \begin{array}{l}
f(5) = ? \\
{\lim }\limits_{x \to 5} f(x) = ? \\
\end{array}\)

If you do and you understand continuity you will see the answer to the question.
 
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