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September 14, 2014

September 14, 2014

Posted by **Anonymous** on Friday, February 11, 2011 at 12:18pm.

f(x) = -1/2(x^2)

- calculus please help -
**helper**, Friday, February 11, 2011 at 1:35pmf(x) = -1/2(x^2)

Step 1

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

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

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

Step 2

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

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

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

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

Step 3

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

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

Step 4

Evaluate lim h-->0

lim h-->0 = -x - 1/2 (0)

lim h-->0 = -x

Dx(-1/2 x^2) = -x

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