No its xto power6 over xtopower10

Question

ScanSolve AI Tutor · Accepted Answer

My apologies for the misunderstanding! You are absolutely right. Let's re-evaluate the limit with the correct numerator.

i. Evaluate $\lim_{x \to 1} \frac{x^6 - 1}{x^{10} - 1}$

Check the form of the limit.
If we substitute $x=1$ into the expression, we get $\frac{1^6 - 1}{1^{10} - 1} = \frac{0}{0}$ , which is an indeterminate form. We can apply L'Hôpital's Rule.
Apply L'Hôpital's Rule.
Take the derivative of the numerator and the derivative of the denominator with respect to $x$ .
Derivative of the numerator: $\frac{d}{dx}(x^6 - 1) = 6x^5$
Derivative of the denominator: $\frac{d}{dx}(x^{10} - 1) = 10x^9$
Evaluate the limit of the new expression.
$\lim_{x \to 1} \frac{6x^5}{10x^9}$
Substitute $x=1$ :
$\frac{6(1)^5}{10(1)^9} = \frac{6}{10} = \frac{3}{5}$
The limit exists and is:
$\frac{3}{5}$

Answer