7 of 13 this quiz: 20 point(s) possible this question: 1 point(s) possible use lhôpitals rule to evaluate…

7 of 13 this quiz: 20 point(s) possible this question: 1 point(s) possible use lhôpitals rule to evaluate lim x→10 x - 10 / x² - 100. then determine the limit using limit laws and commonly known limits. use lhôpitals rule to rewrite the given limit so that it is not an indeterminate form. lim x→10 x - 10 / x² - 100 = lim x→10

7 of 13 this quiz: 20 point(s) possible this question: 1 point(s) possible use lhôpitals rule to evaluate lim x→10 x - 10 / x² - 100. then determine the limit using limit laws and commonly known limits. use lhôpitals rule to rewrite the given limit so that it is not an indeterminate form. lim x→10 x - 10 / x² - 100 = lim x→10

Answer

Explanation:

Step1: Check indeterminate - form

When (x\rightarrow10), (\frac{x - 10}{x^{2}-100}) is in the (\frac{0}{0}) form since (10 - 10=0) and (10^{2}-100 = 0).

Step2: Apply L'Hopital's Rule

Differentiate the numerator and denominator. The derivative of (y=x - 10) is (y^\prime=1), and the derivative of (y=x^{2}-100) is (y^\prime = 2x). So (\lim_{x\rightarrow10}\frac{x - 10}{x^{2}-100}=\lim_{x\rightarrow10}\frac{1}{2x}).

Step3: Evaluate the limit

Substitute (x = 10) into (\frac{1}{2x}). We get (\frac{1}{2\times10}=\frac{1}{20}).

Answer:

(\frac{1}{20})