Let a0,a1,a2,a3......,an be constant such that a0+a1/2+a2/3+.......+an/n+1=0 prove that there exists a real number x belongs to (0,1) such that a0+a1x+a2x^2+.....+anx^n=0

 

Class 12 Math Rolle's Theorem Question

 

Class 12 | In the mean value theorem f(a+h) = f(a) + hf(a+thetah) If f(x) = sqrt(x) find theta

 

Class 12 Rolle's Theorem | If the equation 2x⁴+x³-2x-1=0 has two real root alpha and beta then between alpha and beta the equation 8x³+3x²-2=0 has at least one root

 

Examine the validity and conclusion of Rolle's theorem for the function : f(x) = ex . sin x , for all x belongs to [0, π]