## johnny101 2 years ago Calc, help! How do I determine at what points y=x+2/cos x is continuous?

1. Decart

where the function is defined

2. pgpilot326

what's the def of continuous?

3. Decart

not at asymptote

4. johnny101

its not defined in text so yeah im assuming

5. pgpilot326

Definition in terms of limits of functions The function f is continuous at some point c of its domain if the limit of f(x) as x approaches c through the domain of f exists and is equal to f(c).[2] In mathematical notation, this is written as $\lim_{x \to c}{f(x)} = f(c).$ In detail this means three conditions: first, f has to be defined at c. Second, the limit on the left hand side of that equation has to exist. Third, the value of this limit must equal f(c).

6. Decart

as x approaches what value is the function undefined

7. Decart

take the derivative

8. johnny101

can you walk me through that step by step if possible? I missed the lecture and am somewhat lost

9. Decart

you need to use the quotient rule and the derivative of cos is -sin

10. johnny101

f(x)/g(x)=l/m?

11. pgpilot326

the function is not defined when $x=\frac{ \pi }{ 2 }+k\pi\text{, where }k \in \mathbb{Z}$

12. pgpilot326

because cos x will be 0 at those values of x and the function will not be deifned there. thus, the function will be discontinuous at those points

13. johnny101

so what you have above pi/2+ k(pi), how did you determine points off that?

14. pgpilot326

y = x is continuous for all real x. y = 2/x is continuous for all real x where x is not 0. -1 <= cos x <= 1 for all real x. thus, so long as cos x not = 0, your function will be continuous.

15. johnny101

ohhhhh. Ok I got it now. Thank you!