Final answer:
The limit of (tanx - 1)/(x - π/4) as x approaches π/4 is evaluated using L'Hopital's Rule, resulting in a limit of 2.
Step-by-step explanation:
The student asked to evaluate the limit of the function tan(x) - 1 over x - π/4 as x approaches π/4. This is a standard calculus problem that involves finding the value to which the function approaches as the variable approaches a particular point.
To solve this, we can apply the L'Hopital's Rule since the direct substitution would result in an indeterminate form of 0/0.
First, take the derivative of the numerator and the derivative of the denominator. The derivative of tan(x) is sec2(x), and the derivative of 1 is 0. The derivative of x is 1, and the derivative of π/4 is 0 since it is a constant. Thus, the problem reduces to evaluating the limit of sec2(x) as x approaches π/4.
Substituting π/4 into sec2(x), we find sec2(π/4) = 2, as sec(π/4) = √2. Therefore, the limit is 2.