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lim h -> 0 ?

Answer 1

Paisley Johnson

#9#

#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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Answer 2

Samantha Adkison

The question you have asked is not complete. In order to provide an accurate answer, I need more information about the function or expression for which you are seeking the limit as h approaches 0. Please provide the specific function or expression so that I can assist you further.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

lim h -&gt; 0 ?

lim h -> 0 ?