anonymous
  • anonymous
Calc, help! How do I determine at what points y=x+2/cos x is continuous?
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
where the function is defined
anonymous
  • anonymous
what's the def of continuous?
anonymous
  • anonymous
not at asymptote

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anonymous
  • anonymous
its not defined in text so yeah im assuming
anonymous
  • anonymous
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).
anonymous
  • anonymous
as x approaches what value is the function undefined
anonymous
  • anonymous
take the derivative
anonymous
  • anonymous
can you walk me through that step by step if possible? I missed the lecture and am somewhat lost
anonymous
  • anonymous
you need to use the quotient rule and the derivative of cos is -sin
anonymous
  • anonymous
f(x)/g(x)=l/m?
anonymous
  • anonymous
the function is not defined when \[x=\frac{ \pi }{ 2 }+k\pi\text{, where }k \in \mathbb{Z}\]
anonymous
  • anonymous
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
anonymous
  • anonymous
so what you have above pi/2+ k(pi), how did you determine points off that?
anonymous
  • anonymous
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.
anonymous
  • anonymous
ohhhhh. Ok I got it now. Thank you!

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