Limit problem: lim x^5 - 32 / x - 2; x > 2

[AGlas9837]

In this problem, I'm asked to complete a table and use the result to estimate the limit, then graph to confirm my result:

lim x^5-32/x-2; x>2

The x-values of the table which are given are 1.9, 1.99, 1.999, 2, 2.001, 2.01 and 2.1. I am asked to give the value of f(x) when x=2.

I understand how to use the calculator, plugging in the equation and setting up the table, etc. but am having trouble getting to the correct equation. I factored out x-2 in the denominator which left x^4-16 or (x^2-4)(x^2+4). Using either of these gives 0 when x=2 so I know my answer is incorrect.

 

[pka]

Re: Limit problem

I factored out x-2 in the denominator which left x^4-16 or (x^2-4)(x^2+4). ????

\(\displaystyle \frac{{x^5 - 32}}{{x - 2}} = x^4 + 2x^3 + 4x^2 + 8x + 16\)

 

[kasie-tutor]

I factored out x-2 in the denominator which left x^4-16 or (x^2-4)(x^2+4).

Dear AGlas9837,

Remember that you can't cancel terms, you can only cancel factors. Use polynomial long or synthetic division to simplify.

 

[AGlas9837]

Thank you!