Home
Class 12
MATHS
Prove that ln (1+1/x) gt (1)/(1+x), x g...

Prove that `ln (1+1/x) gt (1)/(1+x), x gt 0`. Hence, show that the function `f(x)=(1+1/x)^(x)` strictly increases in `(0, oo)`.

Promotional Banner

Topper's Solved these Questions

  • MONOTONOCITY

    MOTION|Exercise Exercise - 1 ( Objective Problems ) (SECTION-A ) ( FINDING INTERVALS OF MONOTONOCITY)|7 Videos

  • MONOTONOCITY

    MOTION|Exercise Exercise - 1 ( Objective Problems ) ( SECTION -B ) (FINDING VALUE OF VARIABLE GIVEN MONOTONIC BEHAVIOUR )|2 Videos

  • METHOD OF DIFFERENTIATION

    MOTION|Exercise EXERCISE - 4 LEVEL -II|5 Videos

  • PARABOLA

    MOTION|Exercise EXERCISE - IV|33 Videos

Similar Questions

Explore conceptually related problems

Show that the function f(x) = 2x+1 is strictly increasing on R.

Show that the function f(x)=a^(x),a>1 is strictly increasing on R.

Prove that the function f(x)=[x]-x is strictly decreasing on [0,1).

Prove that the function f(x)=(log)_(e)x is increasing on (0,oo)

Prove that function f(x)=log_(e)x is strictly increasing in the interval (0,oo)

Prove that function f(x)=log_(e)x is strictly increasing in the interval (0,oo)

The function x-((log(1+x))/(x))(x>0) is increasing in:

Prove that the function f(x)=log_(e)(x^(2)+1)-e^(-x)+1 is strictly increasing AA x in R.

Without using the derivative,show that the function f(x)=|x| is strictly increasing in (0,oo) strictly decreasing in (-oo,0)

(log x)^(log x),x gt1