Question

Complete the table. (Round your answers to four decimal places.)

lim x→4 x - 4/x² - 5x + 4

x 3.9 3.99 3.999 4 4.001 4.01 4.1
f(x)

Answer 1

The student must calculate the limit of the function as x approaches 4, which can be simplified to 1/(x - 1) and results in a limit of 1/3 when x is exactly 4.

Step-by-step explanation:

The student is asked to compute the limit of f(x) as x approaches 4 for the function f(x) = (x - 4)/(x² - 5x + 4). This involves substituting the values of x given in the table into the function and rounding the results to four decimal places. To handle the case where x is exactly 4, we need to apply l'Hôpital's rule or factorize the function's numerator and denominator to find the limit.

Upon factorization, the function simplifies to f(x) = 1/(x - 1) when x ≠ 4, and therefore the limit as x approaches 4 is f(4) = 1/(4 - 1) = 1/3.