Can Function Limits Vary with Different Approaching Values?

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Function limits can indeed vary based on different approaching values, as demonstrated in calculus. The original poster seeks to prove or disprove specific statements related to limits, indicating a need for examples or counterexamples. The discussion emphasizes that providing an attempted solution is essential for receiving assistance. This highlights the importance of understanding the fundamental concepts of limits in calculus. Engaging with the material and showing effort is crucial for effective learning and support.
Abukadu
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Good morning from Israel :smile:

I'm a first year student learning about function limits.. I need to prove / disprove the following statements which I got a bit tangled up with..



" Prove or disprove with a contradictory example "

http://img386.imageshack.us/img386/7942/11qd2.jpg
http://g.imageshack.us/img386/11qd2.jpg/1/



http://img384.imageshack.us/img384/9752/22gq6.jpg
http://g.imageshack.us/img384/22gq6.jpg/1/

Thanks !
 
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good afternoon from sweden.

Now this is calculus math, not precalc

Second, you need to show attempt to solution before you will get help.
 

Thread 'Greatest possible value of a constant in polynomial'

Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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