HS Calculus

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Have some more that I do not understand.

Limit theta approaching zero
SinTheta minus Tan theta/ sin cubed theta

  • HS Calculus -

    Rewrite as [sin x(1 - 1/cosx)]/sin^3x
    = [1 - (1/cosx)]/[1 - cos^2x]
    Now use L'Hopital's rule and take the ratio of the derivatives of numerator and denominator. That lets you get rid of the 1's.
    You are left with
    Lim [-tanx secx/(2cosx sinx)]
    = Lim -1/(2 cos^3x)
    Which is -1/2

  • HS Calculus -

    It took me a while to get that one. I cheated and used a hand calculator first, and it agrees.

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