Find the difference quotient fx 1x2Solution81 fx x2 4 fxh

Find the difference quotient f(x) = 1/x^2

Solution

81 . f(x) = x^2 -4

f(x+h) = (x+h)^2 - 4

f(x+h) -f(x) = (x+h)^2 - 4 - ( x^2 -4)

= h^2 +2hx

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

85. f(x) = 1/x^2

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

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

8) f(x) = sqrt(x -2)

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

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

Rationalsing the umerator :

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

= 1/[sqrt(x +h -2) + sqrt(x -2)]