Continuity of Functions

​Pull out your notebook and take notes while you page through the slides.

​Remember, To find discontinuities, set the denominator equal to 0.

​Set any denominators = to 0

​Remember cotx = cosx/sinx

​Try these two problems and check your answers on the next slide!

Multiple Choice

Find the discontinuities of f(x) = secx

• 
  $$x=\frac{n\pi}{2},\ n\ is\ even$$

• $$x\ =\ n\pi,\ n\ is\ even$$

• $$x=\frac{n\pi}{2},\ n\ is\ odd$$

• $$x=n\pi,\ n\ is\ even$$

​Find the discontinuities and determine if they are removable or nonremovable.

​

Find the discontinuities and determine if they are removable or nonremovable.

Multiple Choice

Find the discontinuities of cos(x² - 2)

• x = $$\sqrt[]{2}$$

• none

• x= $$\pm\sqrt[]{2}$$

• $$x=\frac{n\pi}{2}+2\pi n$$

Multiple Choice

Find the discontinuties

$$f\left(x\right)=\frac{1}{\sin x-1}$$

• x = $$\frac{\pi}{2}+2\pi n$$

  $$x=\frac{3\pi}{2}+2\pi n$$

  n is an integer

• $$x=\frac{\pi}{2}+2\pi n$$

  n is an integer

• $$x=n\pi$$ ,

  n is an integer

• $$x\ =\ 0\ +2\pi n$$

  $$x=\pi\ +2\pi n$$

  n is an integer