use lhopitals rule to evaluate lim(x→10) (x - 10)/(x² - 100). then determine the limit using limit laws and…

use lhopitals rule to evaluate lim(x→10) (x - 10)/(x² - 100). then determine the limit using limit laws and commonly known limits. use lhopitals rule to rewrite the given limit so that it is not an indeterminate form. lim(x→10) (x - 10)/(x² - 100)=lim(x→10) (). choose the limit equivalent to the given limit that can be evaluated using limit laws and commonly known limits. a. lim(x→10) 1/(x + 10) b. lim(x→10) 1/(x - 10) c. lim(x→10) x/x² 1/x - 10/x²

use lhopitals rule to evaluate lim(x→10) (x - 10)/(x² - 100). then determine the limit using limit laws and commonly known limits. use lhopitals rule to rewrite the given limit so that it is not an indeterminate form. lim(x→10) (x - 10)/(x² - 100)=lim(x→10) (). choose the limit equivalent to the given limit that can be evaluated using limit laws and commonly known limits. a. lim(x→10) 1/(x + 10) b. lim(x→10) 1/(x - 10) c. lim(x→10) x/x² 1/x - 10/x²

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: Simplify the original - function

Factor the denominator (x^{2}-100=(x + 10)(x - 10)). Then (\frac{x - 10}{x^{2}-100}=\frac{x - 10}{(x + 10)(x - 10)}=\frac{1}{x + 10}) for (x\neq10).

Answer:

A. (\lim_{x\rightarrow10}\frac{1}{x + 10})