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Math Help - Calculas- limits

  1. #1
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    Post Calculas- limits

    Apply limit laws to evaluate or show that the limit does not exist.

    lim Cos (π + ∆ x) +1
    [IMG]file:///C:/DOCUME%7E1/Shayan/LOCALS%7E1/Temp/moz-screenshot-7.jpg[/IMG]∆x -> 0 ∆x


    I started like this but It didnt go anywhere:

    lim Cos (π + ∆ x) +1 . Cos (π + ∆ x) -1= lim Cos (π + ∆ x)^2 -1
    [IMG]file:///C:/DOCUME%7E1/Shayan/LOCALS%7E1/Temp/moz-screenshot-7.jpg[/IMG]∆x -> 0 ∆xCos (π + ∆ x) -1 ∆x -> 0 ∆x(Cos(π + ∆ x) -1

    please help me thanks
    [IMG]file:///C:/DOCUME%7E1/Shayan/LOCALS%7E1/Temp/moz-screenshot-5.jpg[/IMG][IMG]file:///C:/DOCUME%7E1/Shayan/LOCALS%7E1/Temp/moz-screenshot-6.jpg[/IMG]
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  2. #2
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    \lim _{\Delta x \to 0} \frac{{\cos \left( {\pi  + \Delta x} \right) + 1}}{{\Delta x}} = \lim _{\Delta x \to 0} \frac{{\cos \left( \pi  \right)\cos \left( {\Delta x} \right) - \sin (\pi )\sin \left( {\Delta x} \right) + 1}}{{\Delta x}}<br />

    \lim _{\Delta x \to 0} \frac{{\cos \left( {\pi  + \Delta x} \right) + 1}}{{\Delta x}} = \lim _{\Delta x \to 0} \frac{{ - 1\left[ {\cos \left( {\Delta x} \right) - 1} \right]}}{{\Delta x}}<br />
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