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NDA 2020
Exam
NDA
Year
2020
Subject
Mathematics
Chapter
Application of Derivatives

NDA 2020 · Mathematics · Application of Derivatives

Consider the following statements : 1. The function f(x)= x...

Consider the following statements : 1. The function f(x)=ln⁡xf(x)=\ln x increases in the interval (0,∞)(0, \infty). 2. The function f(x)=tan⁡xf(x)=\tan x increases in the interval \left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$. Which of the above statements is/are correct?

Options

  1. A1 only
  2. B2 only
  3. CBoth 1 and 2
  4. DNeither 1 nor 2

Correct answer

C. Both 1 and 2

Step-by-step solution

(1) Graph of f(x)=ln⁡(x)f(x)=\ln (x)
This is increasing function in the interval (0,∞)(0, \infty). (2) Graph of f(x)=tan⁡xf(x)=\tan x.
This is also increasing in (−π2,π2)\left(-\frac{\pi}{2}, \frac{\pi}{2}\right).
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