2U Math - Functions (1 Viewer)

[beve]

Well, I missed one of the intro lessions to functions due to a school leaders thing and i'm doing some catchup on functions. Just checking if i'm getting this right.

Find f(x+h) - f(x) if:

f(x) = 1 - x^2

f(x+h) = 1 - (x+h)^2
f(x+h) = 1 - (x+h)(x+h)
f(x+h) = 1 - (x^2 + 2xh + h^2)

so

f(x+h) - f(x) = 1- (x^2 +2xh + h^2) - (1 - x^2)
f(x+h) - f(x) = 1- x^2 - 2xh - h^2 - 1 + x^2
f(x+h) - f(x) = -2xh - h^2

is this right? or have i gone astray?

 

[a-n-d-r-e-w]

no you've done that correctly

 

[beve]

Cheers brother.

 

[Aerath]

Looks about right to me.
Although, I confess, I never knew that was functions - looks sorta like differentiation from first principles to me. =\

 

[beve]

Well it's just been taught to us as functions but it's leadup work to calculus apparently. Dunno.

 

[kurt.physics]

Well it's just been taught to us as functions but it's leadup work to calculus apparently. Dunno.

Yeh, thats right. The only next step for it to be calculus is to divide by h and find the limit as h-->0.

 

[fjnpenguin]

i love functions

 

[Aerath]

i love functions

Yeah, as do I.

 

[kurt.physics]

Im in the same boat !

 

[minijumbuk]

:O

Looks like differentiation by first principles but without the lim h->0 and divide by h =O