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# Strange answer when finding limit

+3
243
4

Why do I get a strange answer when I plug in x=-1.001 in this function (-1.001^6-1)/(-1.001^3+1) as x--> -1

I get 600 something, but I know I should get a small integer like -2 or something.

Guest Oct 6, 2014

#2
+85918
+16

I think you want to evaluate this, if I'm not mistaken....

lim  (x^6 -1) / (x^3 + 1)

x → -1

Factor (x^6 -1) as (x^3 - 1) (x^3 + 1)   ...  so we have ....

lim  [(x^3 - 1)(x^3 + 1)] /((x^3 + 1)

x → -1

Simplify  by "cancelling" the (x^3 + 1) terms

lim  (x^3 - 1)

x → -1

Now, take the limit

[ (-1)^3 - 1] =  [-1 -1 ] = -2

CPhill  Oct 6, 2014
Sort:

#1
+92253
+6

Your question doesn't make sense because your expression only has numbers in it.  It has no letters so it cannot be a function.  There is nowhere to sub  x=anything in because there is no x!

This is the value of the numerical expression.

$${\frac{\left({\mathtt{\,-\,}}{{\mathtt{1.001}}}^{{\mathtt{6}}}{\mathtt{\,-\,}}{\mathtt{1}}\right)}{\left({\mathtt{\,-\,}}{{\mathtt{1.001}}}^{{\mathtt{3}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}\right)}} = {\mathtt{668.003\: \!447\: \!223\: \!296\: \!296\: \!3}}$$

Melody  Oct 6, 2014
#2
+85918
+16

I think you want to evaluate this, if I'm not mistaken....

lim  (x^6 -1) / (x^3 + 1)

x → -1

Factor (x^6 -1) as (x^3 - 1) (x^3 + 1)   ...  so we have ....

lim  [(x^3 - 1)(x^3 + 1)] /((x^3 + 1)

x → -1

Simplify  by "cancelling" the (x^3 + 1) terms

lim  (x^3 - 1)

x → -1

Now, take the limit

[ (-1)^3 - 1] =  [-1 -1 ] = -2

CPhill  Oct 6, 2014
#3
+3

CPHill, thank you. Even though I forgot to write the correct function you understood and gave me a satisfying answer. Bless you.

Guest Oct 6, 2014
#4
+92253
+3

Edited:  Thank you Chris, I can see where you get that from. I guess I did not give enough thought to the wording of the question.

Melody  Oct 6, 2014

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