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lim h -> 0 ?

1 Answer

Jan 15, 2017

#9#

Explanation:

#f(x)=abs(-9x-7)=abs(9x+7)#

#(f(6+h)-f(6))/h=(abs(9(6+h)+7)-abs(9xx6+7))/h=#
#(abs(61+9h)-61)/h = 9((abs(61/9+h)-61/9)/h)#

now

a) if #h > 0->abs(61/9+h)=61/9+h# so
#9((abs(61/9+h)-61/9)/h)=9(61/9+h-61/9)/h=9#

b) if #h < 0->abs(61/9-h)=61/9-h# so
#9((abs(61/9+h)-61/9)/h)=9(61/9-h-61/9)/(-h)=9#

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