suppose we want to find lim x→4 (x² + 3x - 28)/(x² - 11x + 28). if x = 4, the numerator is 0 and the…

suppose we want to find lim x→4 (x² + 3x - 28)/(x² - 11x + 28). if x = 4, the numerator is 0 and the denominator is 0. this means the limit is 0 the question is wrong the limit is undefined an algebraic reduction is possible

suppose we want to find lim x→4 (x² + 3x - 28)/(x² - 11x + 28). if x = 4, the numerator is 0 and the denominator is 0. this means the limit is 0 the question is wrong the limit is undefined an algebraic reduction is possible

Answer

Explanation:

Step1: Factor the numerator

Factor $x^{2}+3x - 28=(x + 7)(x - 4)$

Step2: Factor the denominator

Factor $x^{2}-11x + 28=(x - 4)(x - 7)$

Step3: Simplify the rational - function

$\lim_{x\rightarrow4}\frac{x^{2}+3x - 28}{x^{2}-11x + 28}=\lim_{x\rightarrow4}\frac{(x + 7)(x - 4)}{(x - 4)(x - 7)}=\lim_{x\rightarrow4}\frac{x + 7}{x - 7}$ (for $x\neq4$)

Answer:

D. An algebraic reduction is possible