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

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Decart
 one year ago
Best ResponseYou've already chosen the best response.0where the function is defined

pgpilot326
 one year ago
Best ResponseYou've already chosen the best response.1what's the def of continuous?

johnny101
 one year ago
Best ResponseYou've already chosen the best response.0its not defined in text so yeah im assuming

pgpilot326
 one year ago
Best ResponseYou've already chosen the best response.1Definition 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).

Decart
 one year ago
Best ResponseYou've already chosen the best response.0as x approaches what value is the function undefined

johnny101
 one year 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

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

pgpilot326
 one year ago
Best ResponseYou've already chosen the best response.1the function is not defined when \[x=\frac{ \pi }{ 2 }+k\pi\text{, where }k \in \mathbb{Z}\]

pgpilot326
 one year ago
Best ResponseYou've already chosen the best response.1because 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

johnny101
 one year 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?

pgpilot326
 one year ago
Best ResponseYou've already chosen the best response.1y = 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.

johnny101
 one year ago
Best ResponseYou've already chosen the best response.0ohhhhh. Ok I got it now. Thank you!
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