For all $x∈ (0,1)$ - CUETMOCK

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Relations and Functions

Question:

For all $x∈ (0,1)$

Options:

$e^x<1+x$

$\log_e(1+x)<x$

$\sin x>x$

$\log_e x>x$

Correct Answer:

$\log_e(1+x)<x$

Explanation:

$e^x=1+x+\frac{x^2}{2!}+.....>1+x⇒x>\log_e(1+x)$ i.e., $\log_e(1+x)<x$

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