Differentiationg: solve lim x-1(x^(3)-1/(e^(1-x)-1)

[Mr B]

Good day may you please kindly help me with solving this "limit"-lim x-1(x^(3)-1/(e^(1-x)-1).The answer i got is zero but i dont think its appropriate to get a zero,for lack of a better word.

 

[Deleted member 4993]

Good day may you please kindly help me with solving this "limit"-lim x-1(x^(3)-1/(e^(1-x)-1).The answer i got is zero but i dont think its appropriate to get a zero,for lack of a better word.

How did you get the answer to be zero (which may be correct)?

Why are you doubting the answer you derived?

Please share your work.

 

[Mr B]

Limits

How did you get the answer to be zero (which may be correct)?

Why are you doubting the answer you derived?

Please share your work.

This is how i got it-lim x=1(lim x^3)-(lim 1)/(e^(1-x)-1) =(1^3)-1/(1-1) and this is how i got a zero,but i strongly feel that there is a certain way to work it out to avoid getting an answer that is zero.Please help enlighten me if you may.

 

[stapel]

This is how i got it-lim x=1(lim x^3)-(lim 1)/(e^(1-x)-1) =(1^3)-1/(1-1) and this is how i got a zero...

Your "work" is cryptic. It would help if you used standard terminology and showed your steps clearly. I think you may mean something along the lines of the following:

I am trying to find the value of the following limit:

. . . . .\(\displaystyle \lim_{x\, \rightarrow\, 1}\, \dfrac{x^3\, -\, 1}{e^{1\, -\, x}\, -\, 1}\)

To evaluate, I plugged 1 in for x:

. . . . .\(\displaystyle \dfrac{1^3\, -\, 1}{1\, -\, 1}\, =\, \dfrac{0}{0}\, =\, 0\)

This is how I got a limit value of zero, but I think there may be something wrong with this.

If this is what you meant, then yes, there is something badly wrong with this.

One can evaluate a limit by "plugging in" only when the expression is defined at the plug-in value. Since, in your case, the expression creates division by zero (which is never defined) and the "zero over zero" expression (which is "indeterminant"), this clearly violates the conditions for "plug-n-chug".

Instead, you will need to use what they've taught you about manipulating expressions for taking limits. What methods have they given you for this sort of thing?