Home
Class 11
MATHS
For the function f(x)= (x^(100))/(100)+(...

For the function `f(x)= (x^(100))/(100)+(x^(99))/(99)+….+(x^(2))/(2)+x+1` Prove that f'(1) =100 f'(0).

Text Solution

Verified by Experts

The correct Answer is:
1
Promotional Banner

Topper's Solved these Questions

  • LIMITS AND DERIVATIVES

    OMEGA PUBLICATION|Exercise IMPORTANT QUESTIONS FROM MISCELLANEOUS EXERCISE|9 Videos
  • LIMITS AND DERIVATIVES

    OMEGA PUBLICATION|Exercise MULTIPLE CHOICE QUESTION|26 Videos
  • CONIC SECTIONS

    OMEGA PUBLICATION|Exercise Multiple Choice Questions (MCQs)|26 Videos
  • LINEAR INEQUALITIES

    OMEGA PUBLICATION|Exercise Multiple Choice Questions |15 Videos

Similar Questions

Explore conceptually related problems

For the function f(x)= x^100/100+x^99/99+...+x^2/2+x+1 . Prove that f'(1)=100f'(0) .

A function y=f(x) satisfies (x+1)f^(')(x)-2(x^(2)+x)f(x) = e^(x^(2))/(x+1), Aax gt -1 . If f(0)=5 , then f(x) is

Find the domain f(x)=log_(100x)((2 log_(10) x+1)/-x)

Let f (x) =(ax+b)/(x+1), lim_(x rarr 0)f(x)=2 and lim_(x to oo)f(x)=1 , Prove that f (- 2) = 0.

Let f(x)=int(x^(2)dx)/((1+x^(2))(1+sqrt(1+x^(2))))and f(0)=0. f(1) is

Find the derivative of the function : f (x) = 2x^2+3x-5 at x=- 1. Also prove that f'(0)+3f' (-1) =0 .

If f(x) =x+1/x , prove that : [f(x)]^3 = f(x^3)+3f (1/x) .

If the functions f(x)=x^(3)+e^(x//2) " and " g(x)=f^(-1)(x) , the value of g'(1) is ………… .

Let f:R→R be a function as f(x)=(x-1)(x+2)(x-3)(x-6)-100. If g(x) is a polynomial of degree ≤3 such that ∫ g(x) f(x) dx does not contain any logarithm function and g(-2)=10. Then