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Hello,

I am working on my calc 1 homework where we use L'Hôpital's rule to evaluate limits. When I try to evaluate this problem to find the indeterminate form, it becomes undefined so I know I need to rewrite it in a different way, I just don't know how. All help is appreciated!

lim 1+(1/√x)
x→0 —————
cot x

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2 answers
  1. lim 1+(1/√x)/cot x
    x→0

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  2. So, you have (1 + 1/√x)/cot x
    As x→0, that goes to ∞/∞
    So, if we try derivatives, we always get the same dang ∞/∞
    So, let's rewrite things as
    tanx (1+√x) / √x
    Now as x→0, that goes to 0/0
    Trying derivatives now, we get
    [sec^2x(1+√x) + tanx(2/√x)] / (2/√x)
    = sec^2x(1+√x)/(2/√x) + tanx*(2/√x) / (2/√x)
    = [√x sec^2x(1+√x)]/2 + tanx
    That goes to 0

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