The desired limit represents the logarithm of an indeterminate form, so L'Hopital's rule could be applied. However, the logarithm can be simplified to a form that is not indeterminate.

<h3>Limit</h3>

We can cancel factors of (x-1), which are what make the expression indeterminate at x=1. Then the limit can be evaluated directly by substituting x=1.

$\diplaystyle \lim\limits_{x\to1}{(\ln(x^5-1)-\ln(x^3-1))}=\lim\limits_{x\to1}\ln{\left(\dfrac{x^5-1}{x^3-1}\right)}\\\\=\lim\limits_{x\to1}\ln\left(\dfrac{x^4+x^3+x^2+x+1}{x^2+x+1}\right)=\ln{\dfrac{5}{3}}$

8 0

1 year ago

PLEASE HELP!Choose the slope and y-intercept that

meriva

The slope is -3/2 and the y-intercept is -3. If you need me to explain I can do that :) hope this helps

3 0

3 years ago

Which numbers line correctly shows 4.5 - 2.5.? HELP FAST!!!

ElenaW [278]

Answer:

Step-by-step explanation:

The answer would be the first option because it’s starting at 4.5, and if you subtracted 2.5, you would get the answer of 2, and that’s what the first option shows. Hope this helps!

5 0

2 years ago

Which of these is false?

coldgirl [10]

B. 21,730 is not greater than 22,341.

4 0

3 years ago