What is the value of k for continuity at x = π/4?

[RandomGuy1]

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?

 

[STEMucator]

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?

You should check both sides of the limit using $\frac{1 - tan(x)}{1 - \sqrt{2} sin(x)}$.

This will allow you to figure out what $k$ must be in order for the function to truly be continuous at $x = \pi/4$.