Which of the following inequalities is true for every real number ?

MATHEMATICS · Single correct · CBSE · Mathematics · Introduction to Trigonometry · Introduction to Trigonometry

Problem

Which of the following inequalities is true for every real number

x\neq 0

? (a)

|x\sin(1/x)|\ge |x|

(b)

|x\sin(1/x)|\le \dfrac{1}{|x|}

(c)

|x\sin(1/x)|\le |x|

(d)

|x\sin(1/x)|\le |x|^{2}