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Math Help - 2 limit problems i need help with

  1. #1
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    2 limit problems i need help with

    1) lim of [(2x)/(cos(pie)(x))] as x approaches 1/2 from the left

    2) lim of [(2(tan^2)x)/x] as x approaches 0

    im good till they start throwin trig in the mix. thx for any help and could u pls show me step by step.
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  2. #2
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    For the first limit, what is the numerator equal to when x = 0.5? What about the denominator? When x = 0.49, is the expression positive or negative?
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  3. #3
    Super Member Random Variable's Avatar
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     \lim_{x \to 0} \ 2 \ \frac{\tan^{2}x}{x} = 2 \lim_{x \to 0} \frac{\tan x \tan x}{x} = 2 \Big(\lim_{x \to 0} \tan x \cdot \lim_{x \to 0} \frac{\tan x}{x} \Big)

     = 2 \Big(\lim_{x \to 0} \tan x \cdot  \lim_{x \to 0} \frac{\sin x}{x \cos x} \Big)= 2 \Big( \lim_{x \to 0} \tan x \cdot  \lim_{x \to 0} \frac{\sin x}{x} \cdot  \lim_{x \to 0} \frac{1}{\cos x} \Big)= 2(0)(1)(1) = 0
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  4. #4
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    thx random
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