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# using four step rule in calculus. use the limit definition to compute y=3x^2-x-2

using four step rule in calculus.

use the limit definition to compute y=3x^2-x-2

Posted by user8279914 on July 16, 2013 at 5:09 PM via web and tagged with calculus, math

The request of the problem seems to be incomplete because you maybe need to evaluate the derivative of the given function using limit definition.

`f'(x) = lim_(Delta x -> 0) (f(x + Delta x) - f(x))/(Delta x)`

`f(x + Delta x) = 3(x + Delta x)^2 - (x + Delta x) - 2`

`f(x + Delta x) = 3x^2 + 6x*Delta x + 3Delta^2 x - x - Delta x - 2`

Replacing `3x^2 + 6x*Delta x + 3Delta^2 x - x - Delta x - 2 for f(x + Delta x)` yields:

`f'(x) = lim_(Delta x -> 0) (3x^2 + 6x*Delta x + 3Delta^2 x - x - Delta x - 2 - 3x^2 + x + 2)/(Delta x)`

Reducing duplicate members yields:

`f'(x) = lim_(Delta x -> 0) (6x*Delta x + 3Delta^2 x - Delta x)/(Delta x)`

Factoring out `Delta x` yields:

`f'(x) = lim_(Delta x -> 0) Delta x*(6x + Delta x - 1)/(Delta x)`

Reducing duplicate factors yields:

`f'(x) = lim_(Delta x -> 0) (6x + Delta x - 1)`

Replacing 0 for `Delta x` yields:

`f'(x) = 6x + 0 - 1 => f'(x) = 6x - 1`

Hence, evaluating the derivative of the given function, using limit definition, yields `f'(x) = 6x - 1.`

Posted by sciencesolve on July 16, 2013 at 5:27 PM (Answer #1)