Science

Math

Humanities

... and beyond

Socratic Meta
Featured Answers

Topics

Question #fba02

1 Answer

Feb 8, 2017

1

Explanation:

If #Lim h->0# then #(f(1+h)-f(1))/h# is f'(1)

Since f(x)= x-2, f(1+h)= 1+h-2= h-1
Also f(1) = 1-2= -1

Hence #(f(1+h)-f(1))/h# =#((h-1)- (-1))/h = h/h# =1

f'(1) =1. The slope is therefore 1

Related questions

What is the limit definition of the derivative of the function #y=f(x)# ?
Ho do I use the limit definition of derivative to find #f'(x)# for #f(x)=3x^2+x# ?
How do I use the limit definition of derivative to find #f'(x)# for #f(x)=sqrt(x+3)# ?
How do I use the limit definition of derivative to find #f'(x)# for #f(x)=1/(1-x)# ?
How do I use the limit definition of derivative to find #f'(x)# for #f(x)=x^3-2# ?
How do I use the limit definition of derivative to find #f'(x)# for #f(x)=1/sqrt(x)# ?
How do I use the limit definition of derivative to find #f'(x)# for #f(x)=5x-9x^2# ?
How do I use the limit definition of derivative to find #f'(x)# for #f(x)=sqrt(2+6x)# ?
How do I use the limit definition of derivative to find #f'(x)# for #f(x)=mx+b# ?
How do I use the limit definition of derivative to find #f'(x)# for #f(x)=c# ?

See all questions in Limit Definition of Derivative

Impact of this question

1859 views around the world

You can reuse this answer
Creative Commons License