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johnny101 Group Title

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

  • one year ago
  • one year ago

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  1. Decart Group Title
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    where the function is defined

    • one year ago
  2. pgpilot326 Group Title
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    what's the def of continuous?

    • one year ago
  3. Decart Group Title
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    not at asymptote

    • one year ago
  4. johnny101 Group Title
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    its not defined in text so yeah im assuming

    • one year ago
  5. pgpilot326 Group Title
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    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).

    • one year ago
  6. Decart Group Title
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    as x approaches what value is the function undefined

    • one year ago
  7. Decart Group Title
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    take the derivative

    • one year ago
  8. johnny101 Group Title
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    can you walk me through that step by step if possible? I missed the lecture and am somewhat lost

    • one year ago
  9. Decart Group Title
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    you need to use the quotient rule and the derivative of cos is -sin

    • one year ago
  10. johnny101 Group Title
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    f(x)/g(x)=l/m?

    • one year ago
  11. pgpilot326 Group Title
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    the function is not defined when \[x=\frac{ \pi }{ 2 }+k\pi\text{, where }k \in \mathbb{Z}\]

    • one year ago
  12. pgpilot326 Group Title
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    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

    • one year ago
  13. johnny101 Group Title
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    so what you have above pi/2+ k(pi), how did you determine points off that?

    • one year ago
  14. pgpilot326 Group Title
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    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.

    • one year ago
  15. johnny101 Group Title
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    ohhhhh. Ok I got it now. Thank you!

    • one year ago
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