the limit represents the derivative of some function f(x)

Question

The limit
lim x→1   x^7−1/x−1

represents the derivative of some function f(x) at some number a. Find f and a.

 

f(x)=_____

a=______

 

Answer 1

Hussein,

 

As Kemal stated, you need to use parentheses.  I will assume you meant

 

lim_x→1 [(x⁷ - 1)/(x -1)] = ?

 

This is an indeterminate form.  Use L'Hopital's rule.  Are you familiar with it?

 

lim_x→1 [(x⁷ - 1)/(x -1)] = lim_x→1 (7x⁶ / 1) = 7

 

 

Answer 2

Hi Hussein,

 

Please specify the terms of the function by using parentheses. At this level, this should be standard practice.