Determine (f(x+h) - f(x)) / h , if f(x)=1-x^2?

Answer 1

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

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

[f(x + h) - f(x)] / h
= h(-2x - h) / h
= -2x - h

Answer 2

You left out lim h-->0 in which case the answer is -2x, assuming you are trying to find the derivative.

lim h-->0 [1 - (x + h)² - (1 - x²)] / h
lim h-->0 [1 - (x² + 2xh + h²) - (1 - x²)] / h
lim h-->0 [1 - x² - 2xh - h² - 1 + x²] / h
lim h-->0 [-2xh - h² ] / h
lim h-->0 [h(-2x - h) ] / h
lim h-->0 -2x - h
-2x - 0 =

-2x

Answer 3

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

Answer 4

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

Answer 5

[f(x+h)-f(x)]
now f(x=1-x^2,
f(x+h)=1-(x+h)^2
=1-x^2-h^2-2xh
so
f(x+h)-f(x)
=-2xh-h^2
[f(x+h)-f(x)]/h
=-2x-h/2

When h goes to zero,[f(x+h)-f(x)]/h=-2xwhich is the derivative of f(x)=1-x^2 It is OK.

Answer 6

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

Answer 7

f(x)=1-x^2
so f(x+h)=1-(x+h)^2
& f(x)=1-x^2
so {f(x+h)-f(x)}/h=[1-(x+h)^2-{1-(x)^2}]/h
or ={1-x^2-2xh-h^2-1+x^2}/h
=(-2xh-h^2)/h
=-2x-h ans

Answer 8

-2x

if ur just looking for the first derivative
u will hav to find the limit
and according to the work shown by other users already,
u can just substitute 0 for h
and get -2x

Answer 9

[1-(x+h)^2]-[1-x^2)] /h
[1-x^2-2xh-h^2-1+x^2]/h
[-2xh-h^2]/h
h(-2x-h)/h
(-2x-h)