Understanding Intervals of Continuity

The video tutorial explains how to determine the interval of continuity for given functions over the interval from 0 to 2π radians. It first analyzes a function involving tangent x, identifying points where tangent x is zero or undefined. The tutorial uses both graph and unit circle methods to find these points. It then examines a second function involving quadratic and trigonometric components, focusing on where sine x equals one. The video concludes by stating the intervals of continuity using interval notation.

What is the first condition for the continuity of the function f(x) = (25 - x²) / tan(x)?

• x must be less than 2π

• tan(x) must be zero

• tan(x) must be defined

• x must be greater than zero

Where is the tangent function equal to zero within the interval from 0 to 2π?

• π/3 and 2π/3

• π/4 and 3π/4

• 0, π, and 2π

• π/2 and 3π/2

Which values must be excluded to determine the interval of continuity for f(x)?

• π/3, 2π/3, π

• π/4, π/2, 3π/4

• 0, π/2, π, 3π/2

• π/6, π/2, 5π/6

What is the interval of continuity for the function f(x) = (25 - x²) / tan(x) using interval notation?

• (0, π/3) ∪ (π/3, 2π/3)

• (0, π/2) ∪ (π/2, π) ∪ (π, 3π/2) ∪ (3π/2, 2π)

• (0, π) ∪ (π, 2π)

• (0, π/4) ∪ (π/4, π/2) ∪ (π/2, 3π/4)

What happens to the function f(x) = (25 - x²) / tan(x) at x = π/2?

• It is continuous

• It equals one

• It equals zero

• It is undefined

What is the only restriction for the second function involving x² - 9 and trigonometric functions?

• cos(x) must be zero

• sin(x) must not equal 1

• x must be greater than zero

• x must be less than π

At which angle is the sine function equal to 1 within the interval from 0 to 2π?

• 3π/2

• π

• 2π

• π/2

What is the interval of continuity for the second function using interval notation?

• [0, π/2) ∪ (π/2, 2π)

• (0, π) ∪ (π, 2π)

• [0, π) ∪ (π, 2π]

• (0, π/4) ∪ (π/4, π/2)

Why must x not equal π/2 for the second function?

• Because sin(x) equals 1

• Because sin(x) is undefined

• Because cos(x) equals 1

• Because sin(x) is zero

Which trigonometric function is used to determine where the second function is undefined?

• Cosine

• Tangent

• Sine

• Secant