Calculus

Evaluate the limit as h -> 0 of:

[tan (pi/6 + h) - tan(pi/6)]/h

I thought the answer was √3/3, or tan(pi/6, but apparently that is wrong, any tips here?

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  1. the basic definition of the derivative of any function f(x) is
    Lim [f(x+h) - f(x)]/h as h --> 0

    this is exactly the pattern we are looking at.
    So what they are asking for is the derivative of
    tan x when x = pi/6

    let y = tan x
    then dy/dx = sec^2 x
    = sec^2 (pi/6) or sec^2 30º
    = 4/3

    ( cos 30º = √3/2
    sec 30º = 2/√3
    sec ^2 30º = 4/3 )

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  2. Thanks, I just forgot to do the dy/dx of tan x.

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  3. 12 year old thread but still saved my grade Thanks

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