Continuity math homework

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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?
 

Answers and Replies

  • #2
STEMucator
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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##.
 

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