demonstrate ∣sin(y)−sin(x)∣≤∣y−x∣


Question and Answers Forum

All Questions Topic List
Relation and Functions Questions
Previous in All Question Next in All Question
Previous in Relation and Functions Next in Relation and Functions
Question Number 60203 by meme last updated on 18/May/19

$d e m o n s t r a t e$ $∣ s i n (y) - s i n (x) ∣⩽∣ y - x ∣$
Commented by Mr X pcx last updated on 19/May/19

$l e t f (x) = s i n x w e h a v e f^{,} (x) = c o s x$ $a n d ∣ f^{^{'}} (x) ∣⩽ 1, f i s C^{1} o n R \Rightarrow$ $∣ f (y) - f (x) ∣⩽ 1 \times ∣ y - x ∣$ $(t a f t h e o r e m) \Rightarrow∣ s i n y - s i n x ∣⩽∣ x - y ∣$
	Answered by meme last updated on 18/May/19

	$x, y \in∣ R$
	Answered by kaivan.ahmadi last updated on 19/May/19

	$s u p p o s e t h a t y > x$ $a p p l y i n g t h e m e a n v a l u e t h e o r e m o n [x, y]$ $s i n y - s i n x = (y - x) c o s c f o r s o m e c \in (x, y)$ $n o w s i n c e ∣ c o s c ∣⩽ 1 w e h a v e$ $∣ s i n y - s i n x ∣=∣ y - x ∣∣ c o s c ∣⩽∣ y - x ∣$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum