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Littlebird

  • one year ago

lim x-> pi/2+ (4/x)secx

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  1. geerky42
    • one year ago
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    Because denominator doesn't approach to 0, you can apply quoient rule. Then try to evaluate \(\lim_{x\to\frac\pi2^+}~ \sec x\)

  2. Littlebird
    • one year ago
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    Is the quotient rule where you divide by limits? If so, would I then write lim4/limx *limsecx

  3. Littlebird
    • one year ago
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    I think secx = 1/cosx, and cos(pi/2) = 0, but I then I'm stuck

  4. geerky42
    • one year ago
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    Yeah. I was more look of \(\dfrac4x\sec x = \dfrac{4\sec x}x\), so \(\lim\dfrac{4\sec x}x = \dfrac{\lim 4\sec x}{\lim x}\) Try imagine the graph of sec x, what happen to sec x as x approaches \(\pi/2\) from right side?

  5. Littlebird
    • one year ago
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    It approaches -infinity.

  6. geerky42
    • one year ago
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    Right. and denominator will be just positive value So anything positive multiplied by negative infinity is just negative infinity. Is that clear?

  7. geerky42
    • one year ago
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    Answer is \(\boxed{-\infty}\)

  8. Littlebird
    • one year ago
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    Thanks!

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