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johnny101
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Calc, help! How do I determine at what points y=x+2/cos x is continuous?
 11 months ago
 11 months ago
johnny101 Group Title
Calc, help! How do I determine at what points y=x+2/cos x is continuous?
 11 months ago
 11 months ago

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Decart Group TitleBest ResponseYou've already chosen the best response.0
where the function is defined
 11 months ago

pgpilot326 Group TitleBest ResponseYou've already chosen the best response.1
what's the def of continuous?
 11 months ago

Decart Group TitleBest ResponseYou've already chosen the best response.0
not at asymptote
 11 months ago

johnny101 Group TitleBest ResponseYou've already chosen the best response.0
its not defined in text so yeah im assuming
 11 months ago

pgpilot326 Group TitleBest ResponseYou've already chosen the best response.1
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).
 11 months ago

Decart Group TitleBest ResponseYou've already chosen the best response.0
as x approaches what value is the function undefined
 11 months ago

Decart Group TitleBest ResponseYou've already chosen the best response.0
take the derivative
 11 months ago

johnny101 Group TitleBest ResponseYou've already chosen the best response.0
can you walk me through that step by step if possible? I missed the lecture and am somewhat lost
 11 months ago

Decart Group TitleBest ResponseYou've already chosen the best response.0
you need to use the quotient rule and the derivative of cos is sin
 11 months ago

johnny101 Group TitleBest ResponseYou've already chosen the best response.0
f(x)/g(x)=l/m?
 11 months ago

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

pgpilot326 Group TitleBest ResponseYou've already chosen the best response.1
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
 11 months ago

johnny101 Group TitleBest ResponseYou've already chosen the best response.0
so what you have above pi/2+ k(pi), how did you determine points off that?
 11 months ago

pgpilot326 Group TitleBest ResponseYou've already chosen the best response.1
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.
 11 months ago

johnny101 Group TitleBest ResponseYou've already chosen the best response.0
ohhhhh. Ok I got it now. Thank you!
 11 months ago
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