A function f(x) is defined in the interval [1,4) as follows `f(x)={{:(,log_(e)[x],1 le x lt 3),(,|log_(e)x|,3 le x lt 4):}`. Then, the curve y=f(x)
A. is broken at two points
B. is broken at exactly one point
C. does not have a definite tangent at two points
D. does not have a definite tangent at more than two points

General Awareness CONTINUITY-AND-DIFFERENTIABILITY IN GENERAL AWARENESS . 2 years ago

  1   0   0   0   0 tuteeHUB earn credit +10 pts

5 Star Rating 1 Rating
Correct Answer - A::C
We have
`f(x)={{:(,log_(e)[x],1 le x lt 3),(,|log_(e)x|,3 le x lt 4):}`
`Rightarrow f(x)={{:(,0,1 le x lt 2),(,log_(e)2,2 le x lt 3),(,|log_(e)x|,3 le x lt 4):}`
Clearly, f(x) is everywhere continuous and differentiable except possibility at x=2,3
We observe that `underset(x to 2^(-))lim f(x)=underset(x to2^(-))lim 0=0`
`and underset(x to 2^(+))lim f(x)=underset(x to2^(+))lim log_(e)2=log_(e)2`
Clearly, f(x) is not continuous at x=2
It can be easily seen that f(x) is not continuous at x=3
Hence, f(x) is neither continuous nor differenitable at x=2,3
Thus, the curve y=f(x) is broken at two points and it does not have a definite tangent at these points

Posted on 06 Oct 2022, this text provides information on General Awareness related to CONTINUITY-AND-DIFFERENTIABILITY IN GENERAL AWARENESS. Please note that while accuracy is prioritized, the data presented might not be entirely correct or up-to-date. This information is offered for general knowledge and informational purposes only, and should not be considered as a substitute for professional advice.

Take Quiz To Earn Credits!

Turn Your Knowledge into Earnings.

tuteehub_quiz

Tuteehub forum answer Answers

Post Answer

No matter what stage you're at in your education or career, TuteeHub will help you reach the next level that you're aiming for. Simply,Choose a subject/topic and get started in self-paced practice sessions to improve your knowledge and scores.