If f(x)=1/(x+1)f(x)=1x+1 how do you evaluate (f(x+h)-f(x))/hf(x+h)−f(x)h?

2 Answers
Shwetank Mauria
Aug 2, 2016

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

Explanation:

As f(x)=1/(x+1)f(x)=1x+1, f(x+h)=1/(x+h+1)# and

(f(x+h)-f(x))/hf(x+h)−f(x)h

= (1/(x+h+1)-1/(x+1))/h1x+h+1−1x+1h

= ((x+1-x-h-1)/((x+h+1)(x+1)))/hx+1−x−h−1(x+h+1)(x+1)h

= ((-h)/((x+h+1)(x+1)))/h−h(x+h+1)(x+1)h

= (-h)/((x+h+1)(x+1))xx1/h−h(x+h+1)(x+1)×1h

= (-1)/((x+h+1)(x+1))−1(x+h+1)(x+1)

Ratnaker Mehta
Aug 2, 2016

-1/((x+1)(x+h+1))−1(x+1)(x+h+1)

Explanation:

f(x)=1/(x+1) rArr f(x+h)=1/(x+h+1)f(x)=1x+1⇒f(x+h)=1x+h+1

rArr f(x+h)-f(x)=1/(x+h+1)-1/(x+1)=(x+1-x-h-1)/((x+1)(x+h+1))⇒f(x+h)−f(x)=1x+h+1−1x+1=x+1−x−h−1(x+1)(x+h+1).

=- h/((x+1)(x+h+1))=−h(x+1)(x+h+1)

rArr (f(x+h)-f(x))/h=-cancelh/(cancelh(x+1)(x+h+1))

=- 1/((x+1)(x+h+1)).

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