A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 2 years ago
Calc, help! How do I determine at what points y=x+2/cos x is continuous?
anonymous
 2 years ago
Calc, help! How do I determine at what points y=x+2/cos x is continuous?

This Question is Closed

anonymous
 2 years ago
Best ResponseYou've already chosen the best response.0where the function is defined

anonymous
 2 years ago
Best ResponseYou've already chosen the best response.0what's the def of continuous?

anonymous
 2 years ago
Best ResponseYou've already chosen the best response.0its not defined in text so yeah im assuming

anonymous
 2 years ago
Best ResponseYou've already chosen the best response.0Definition 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).

anonymous
 2 years ago
Best ResponseYou've already chosen the best response.0as x approaches what value is the function undefined

anonymous
 2 years ago
Best ResponseYou've already chosen the best response.0can you walk me through that step by step if possible? I missed the lecture and am somewhat lost

anonymous
 2 years ago
Best ResponseYou've already chosen the best response.0you need to use the quotient rule and the derivative of cos is sin

anonymous
 2 years ago
Best ResponseYou've already chosen the best response.0the function is not defined when \[x=\frac{ \pi }{ 2 }+k\pi\text{, where }k \in \mathbb{Z}\]

anonymous
 2 years ago
Best ResponseYou've already chosen the best response.0because 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

anonymous
 2 years ago
Best ResponseYou've already chosen the best response.0so what you have above pi/2+ k(pi), how did you determine points off that?

anonymous
 2 years ago
Best ResponseYou've already chosen the best response.0y = 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.

anonymous
 2 years ago
Best ResponseYou've already chosen the best response.0ohhhhh. Ok I got it now. Thank you!
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.