Answer to Question #248042 in Calculus for Asma

Question #248042

Determine which of the following functions are of bounded variation on[0,1]

a. f(x)= x^2sin(1/X) if x#0 ,f(0)=0

b. f(x)= √x sinx,if x#0,f(0)=0


1
Expert's answer
2021-10-08T04:40:28-0400

"(a) f(x)=x^2sin(\\frac1x)"

"f(0)=0;f(1)=sin(1)"

In the interval [0,1]:

"0\\leq sin(\\frac1x)\\leq 1"

"0\\leq x^2sin(\\frac1x)\\leq x^2"

So, the function doesn't blow up to infinity, thus, f(x) is bounded.

(b)"f(x)=\\sqrt{x}sin x"

"f(0)=0;f(1)=sin(1)"

"0\\leq sinx \\leq1"

"0\\leq \\sqrt{x}sinx \\leq\\sqrt x"

So, the function doesn't blow up to infinity, thus, f(x) is bounded.


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment

LATEST TUTORIALS
New on Blog
APPROVED BY CLIENTS