Evaluate the limit as h -> 0 of:

Question

[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?

Answer 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 )

Answer 2

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

Answer 3

12 year old thread but still saved my grade Thanks

Answer 4

did not save my grade this is unreadable