SATHEE: Application of Derivatives 2 Question 30

Application of Derivatives 2 Question 30

####30. Show that $2 \sin x + 2 \tan x \geq 3 x$ , where $0 \leq x < π / 2$ .

(1990, 4M)

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Answer:

Correct Answer: 30. (a, c)

Solution:

Let $y = f (x) = 2 \sin x + 2 \tan x - 3 x$

$\Rightarrow f^{'} (x) = 2 \cos x + 2 \sec^{2} x - 3$

For $0 \leq x < π / 2, f^{'} (x) > 0$

Thus, $f (x)$ is increasing.

$\begin{array}{ll} When & x \geq 0, f (x) \geq f (0) \\ \Rightarrow & 2 \sin x + 2 \tan x - 3 x \geq 0 + 0 - 0 \\ \Rightarrow & 2 \sin x + 2 \tan x \geq 3 x \end{array}$

Application of Derivatives 2 Question 30

Answer:

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Application of Derivatives 2 Question 30

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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