The value of k for continuity of the function f(x) = [1 - tan(x)]/[1 - √2 sin(x)] at x = π/4 is determined by ensuring that the limit as x approaches π/4 equals k/2. The limit can be evaluated by checking both sides of the equation, specifically using the expression lim x → π/4 f(x). The correct evaluation leads to the conclusion that k must equal 1 for the function to be continuous at this point.
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RandomGuy1 said:Homework Statement
f(x) = [1 - tan(x)]/[1 - √2 sin(x)] for x ≠ π/4
= k/2 for x = π/4
Find the value of k if the function is continuous at x = π/4
The Attempt at a Solution
This means that lim x → π/4 f(x) = k/2
I put x = (π/4 + h) and then evaluated the limit as h tended to zero. Doesn't work. Get sin (2h) in the denominator. Can I get a hint?