Which of the following is not true `log(1+x)ltx` for `xgt0`

Which of the following is not true log(1+x) 0

Which one of the following is true ? For the real function : f(x)={{:(x+2" if "xle1),(x-2" if "xgt1):} ,

If y+log(1+x)=0 which of the following is true?

[ If xgt0 then which of the following is true 1) tan^(-1)xgt(x)/(1+x^(2)), 2) tan^(-1)x=(x)/(1+x^(2)) 3) tan^(-1)xlt(x)/(1+x^(2)), 4) tan^(-1)x!=(x)/(1+x^(2))]

Let f(x)={{:((e^(x)-1)/(x)",",xgt0),(0",",x=0):} be a real valued function. Which of the following statements is/are correct? 1. f(x) is right continuous at x=0. 2. f(x) is discontinuous at x=1. Seletct the correct answer using the code given below.

Consider the following statements : Statement I : xgtsinx" for all "xgt0 Statement II : f(x)=xsinx is an increasing function for all xgt0 Which one of the following is correct in respect of the above statements?

For x gt 1 and y = log x-(x-1) which one of the following is not true ?

Differentiate each of the following w.r.t. x : (i) sin (logx), x gt0 (ii) log(logx), xgt1

Find the derivative of the following w.r.t. x : log(logx),xgt1

If f(x)={{:(x^(3)(1-x)",",xle0),(xlog_(e)x+3x",",xgt0):} then which of the following is not true?