Application of Derivatives 2 Question 31

####31. Show that 1+xlog(x+x2+1)1+x2x0.

Show Answer

Answer:

Correct Answer: 31. 12π3 (1+π3), 32π6 (1+π6)

Solution:

  1. Let f(x)=1+xlog(x+x2+1)1+x2

f(x)=x1+xx2+1x+x2+1+log(x+x2+1)

xx2+1=xx2+1+log(x+x2+1)xx2+1f(x)=log(x+x2+1)f(x)0[log(x+x2+1)0]

f(x) is increasing for x0.

f(x)f(0)

1+xlog(x+1+x2)1+x21+01

1+xlog(x+1+x2)1+x2,x0



NCERT Chapter Video Solution

Dual Pane