Evaluate the limit of the fraction (f(x)-f(1))/(x-1), if f(x)=1+2x^5/x^2? x->1

Expert Answers

An illustration of the letter 'A' in a speech bubbles

We are given that f(x)=1+2x^5/x^2 = 1 + 2x^3.

We have to find:  lim x -->1 [(f(x) - f(1))/(x-1)]

=> lim x -->1 [(1+ 2x^3 - 1 - 2)/(x-1)]

=> lim x -->1 [(2x^3 - 2)/(x-1)]\

=> lim x -->1 [2*(x - 1)(x^2 + x + 1)/(x-1)]

=> lim x...

Unlock
This Answer Now

Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Start your 48-Hour Free Trial

We are given that f(x)=1+2x^5/x^2 = 1 + 2x^3.

We have to find:  lim x -->1 [(f(x) - f(1))/(x-1)]

=> lim x -->1 [(1+ 2x^3 - 1 - 2)/(x-1)]

=> lim x -->1 [(2x^3 - 2)/(x-1)]\

=> lim x -->1 [2*(x - 1)(x^2 + x + 1)/(x-1)]

=> lim x -->1 [2*(x^2 + x + 1)]

substitute x with 1

=> 2*(1 +1 +1)

=> 6

Therefore the required limit  is 6.

Approved by eNotes Editorial Team