a1tmarqchellAl a1tmarqchellAl

23-09-2016
Mathematics

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lim as x approaches pi/4:
[(tan x - 1)/(x - pi/4)]

The limit represents the derivative of some function f at some number a. State such an f and a.

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HomertheGenius HomertheGenius

28-09-2016

[tex] \lim_{x \to \pi /4} \frac{tan x - 1}{x- \pi /4} = \frac{0}{0} [/tex]
With L` Hospital`s Rule ( ( tan x ) ` = 1/ cos^2 x ) :
[tex] \lim_{x \to \pi /4} \frac{1}{cos ^{2} x} = \\ = \frac{1}{cos ^{2} ( \pi /4)} = \\ \frac{1}{1/2} [/tex] = 2

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