Location Set your Location

Login Ask & Answer Success Stories Courses Tuition & Classes Fees Write a Review All Categories Help Center
Post your Learning Need Signup as a Tutor
✕

Popular Cities

Bangalore Hyderabad Delhi Mumbai Chennai Pune Kolkata Gurgaon Ahmedabad Jaipur Noida
✕

Popular Categories

Class 12 Tuition Class 11 Tuition Class 10 Tuition Class 9 Tuition Spoken English Class 6 to 8 Tuition IELTS Coaching Class 1 to 5 Tuition Java Training Python Training German Language
true
✕

Find the best tutors and institutes for Class 12 Tuition

Find Best Class 12 Tuition

Please select a Category.

Please select a Locality.

No matching category found.

No matching Locality found.

Outside India?
Class 12 Tuition > Class 12 Tuition Questions > differination of |x| in conditions
✕

Search for topics

differination of |x| in conditions

Asked by Last Modified  

Tuition/Class XI-XII Tuition (PUC)

Follow 0
Answer

27 Answers

Please enter your answer

Home Tuitor for Class V to X,Computer,Speaking English,CBSE, ICSE & State Board

Let y = |x| Step 1) Applying first principle ... NOTE:- We shall apply the limit later & now here dx represents delta x. dy/dx = /dx as mentioned we shall apply limit later so currently dy/dx represents Step 2) Multiplying numerator and denominator by we get, /{dx*} Step 3) simplifying... read more
Let y=|x| Step 1) Applying first principle ... NOTE:- We shall apply the limit later & now here dx represents delta x. dy/dx = [|x+dx| -|x|]/dx as mentioned we shall apply limit later so currently dy/dx represents [delta y/ delta x ] Step 2) Multiplying numerator and denominator by [|x+dx| + |x|] we get, [(x+dx)^2-x^2]/{dx*[|x+dx| +|x|]} Step 3) simplifying [2x*dx+(dx)^2]/{dx*[|x+dx| +|x|]} As we have not yet applied the limit we cancel a common dx term from numerator and denominator. Step 4) What remains is [2x+dx]/[|x+dx| +|x|] Step 5) Now we apply the limit of dx tends to zero Therefore, dy/dx = x/|x| Now for x>0, dy/dx = 1 for x<0, dy/dx = -1 at x=0 the function is not differentiable as dy/dx is not defined. read less
Comments
Dislike Bookmark

Mathematics Professor

Since the absolute value is defined by cases, |x|={x?xif x?0;if x0, x0, for ?x sufficiently close to 0 we will have x+?x>0. So f(x)=|x|=x, and f(x+?x)=|x+?x|=x+?x; plugging that into the limit, we have: lim?x?0f(x+?x)?f(x)?x=lim?x?0|x+?x|?|x|?x=lim?x?0(x+?x)?x?x. You should be able to finish it now. For... read more
Since the absolute value is defined by cases, |x|={x?xif x?0;if x<0, it makes sense to deal separately with the cases of x>0, x<0, and x=0. For x>0, for ?x sufficiently close to 0 we will have x+?x>0. So f(x)=|x|=x, and f(x+?x)=|x+?x|=x+?x; plugging that into the limit, we have: lim?x?0f(x+?x)?f(x)?x=lim?x?0|x+?x|?|x|?x=lim?x?0(x+?x)?x?x. You should be able to finish it now. For x<0, for ?x sufficiently close to zero we will have x+?x<0; so f(x)=?x and f(x+?x)=?(x+?x). It should again be easy to finish it. The tricky one is x=0. I suggest using one-sided limits. For the limit as ?x?0+, x+?x=?x>0; for ?x?0?, x+?x=?x<0; the (one-sided) limits should now be straightforward. good luck read less
Comments
Dislike Bookmark

Tutor

Differentiation of |x| is |x|/x , so for positive & negative x you can easily put x with appropriate sign to get the result.
Comments
Dislike Bookmark

B TECH (Electrical)

when x=0- you will get differentiation -1 and when x=0+ you will get differentiation +1 this function is not differentiable at x=0
Comments
Dislike Bookmark

Tutor

Let y=|x|. Step 1 Applying first principle ... NOTE:- We shall apply the limit later. & Currently dx represents delta x. dy/dx=/dx as mentioned we shall apply limit later so currently dy/dx represents Step 2 multiplying numerator and denominator by we get, /{dx*} Step... read more
Let y=|x|. Step 1 Applying first principle ... NOTE:- We shall apply the limit later. & Currently dx represents delta x. dy/dx=[|x+dx| -|x|]/dx as mentioned we shall apply limit later so currently dy/dx represents [delta y/ delta x ] Step 2 multiplying numerator and denominator by [|x+dx| + |x|] we get, [(x+dx)^2-x^2]/{dx*[|x+dx| +|x|]} Step 3 simplifying [2x*dx+(dx)^2]/{dx*[|x+dx| +|x|]} as we have not yet applied the limit we can cancel a common dx term from numerator and denominator. Step 4 What remains is [2x+dx]/[|x+dx| +|x|] Step 5 Now we apply the limit of dx tends to zero Therefore, dy/dx=x/|x| Now for x>0, dy/dx=1 for x<0, dy/dx=-1 at x=0 the function is not differentiable as dy/dx is not defined. read less
Comments
Dislike Bookmark

if x>0 it will be 1 and if x<0 then it will be -1 and at x=0 derivative is not defined.
Comments
Dislike Bookmark

i am a tution teacher

In differination ill give signum function 1when X is positive and -1 when it is negative
Comments
Dislike Bookmark

Teaching is my passion!!!!

if x>0 it will be 1 and if x<0 then it will be -1 and at x=0 derivative is not defined
Comments
Dislike Bookmark

Trainer

(d/dx) IxI = IxI/x, which is not continuous.
Comments
Dislike Bookmark

Ms office, tally,Dot net, C C++ Oracle java,B Tech Tutions,Spoken English,Graphic Design, Tutions for class 1 to B Tech,Abacus,Vedic maths,Bank Coaching,Sainik school entrance exams,Photoshop,Corel Draw,

Conditions under which one may differentiate term by term a convergent sequence of functions are to be found in the literature.f Some of these conditions are obtained as corollaries of theorems about term wise integration, and consequently contain in the hypothesis the assumption that the derived... read more
Conditions under which one may differentiate term by term a convergent sequence of functions are to be found in the literature.f Some of these conditions are obtained as corollaries of theorems about term wise integration, and consequently contain in the hypothesis the assumption that the derived sequence converges. Without this assumption, sufficient conditions for term wise differentiation may be obtained from the fundamental theorem on reversing the order of iterated limits. read less
Comments
Dislike Bookmark

View 25 more Answers

Related Questions

Furqankhan asked Fill in the blanks by suitable conversion of units (a) 1 kg m2 s-2 = �. g cm2 s-2 (b) 1 m =���� ly (c) 3.0 m s-2 = �. km h-2 (d) G = 6.67 x 10-11 N m2 (kg)-2 = �. (cm)3 s-2 g-1
20/09/2018
24
Pradeep asked " Fill in the blanks by suitable conversion of units (a) 1 kg m2 s-2 = �. g cm2 s-2 (b) 1 m =���� ly (c) 3.0 m s-2 = �. km h-2 (d) G = 6.67 x 10-11 N m2 (kg)-2 = �. (cm)3 s-2 g-1."
12/09/2018
26
Sandipan Saha asked

What will be the fees of Computer Science & Application for Class-XI-XII (all board).
26/10/2018
141

Now ask question in any of the 1000+ Categories, and get Answers from Tutors and Trainers on UrbanPro.com

Ask a Question

Related Lessons

Basic Accounting Procedures – II Journal
I. Journalise the following Transactions – Chapter 4 (Book Examples) Jan 1, 2004 – Saravanan started the business with Rs. 1,00,000. Jan 3, 2004 – Received cash from Balan Rs. 25,000 Feb...

Alex J | 04 Aug

0 0
0
Introduction to Chess
Chess is a game played on 64 square board which is a combination of two colours, usually black and white (nowadays different colours chess boards are available like green and white, yellow and brown). The...

Sahil Maurya | 12 Jun

0 0
0
For CBSE PUC Accountancy- How to Identify Revenue vs Capital Expenditures for a Business Organisation
Dear Students, Identification of Revenue and Capital natured expenditure is essential for us. It is the base for many of the chapters in your Accountancy Syllabus. Let us understand these terms with several...

Madhura Sagar G. | 09 Apr

0 0
0

Recommended Articles

Meet Raghunandan.G.H, a B. Tech Tutor from...

Raghunandan is a passionate teacher with a decade of teaching experience. Being a skilled trainer with extensive knowledge, he provides high-quality BTech, Class 10 and Class 12 tuition classes. His methods of teaching with real-time examples makes difficult topics simple to understand. He explains every concept in-detail...

Read full article >

Meet Urmila, an MBBS tutor from Bangalore

Urmila is a passionate teacher with over 8 years of experience in teaching. She is currently pursuing her Ph. D. She provides classes for Class 11, Class 12, MBBS and Medical tuition. Urmila began her career in teaching long before she became a teacher. She used to provide classes for foreign national students in her college...

Read full article >

Meet Radhe Shyam Burman, an MBA Tutor from...

Radhe Shyam is a highly skilled accounts and finance trainer with 8 years of experience in teaching. Accounting is challenging for many students and that s where Radhe Shyam s expertise comes into play. He helps his students not only in understanding the subject but also advises them on how to overcome the fear of accounts...

Read full article >

Meet Swati, a Hindi Tutor from Bangalore

Swati is a renowned Hindi tutor with 7 years of experience in teaching. She conducts classes for various students ranging from class 6- class 12 and also BA students. Having pursued her education at Madras University where she did her Masters in Hindi, Swati knows her way around students. She believes that each student...

Read full article >

Find Class 12 Tuition near you
Class 12 Tuition in Delhi
Class 12 Tuition in Bangalore
Class 12 Tuition in Hyderabad
Class 12 Tuition in Mumbai
Class 12 Tuition in Kolkata
Class 12 Tuition in Chennai
Class 12 Tuition in Pune
Class 12 Tuition in Gurgaon
Class 12 Tuition in Noida
Class 12 Tuition in Ghaziabad

Looking for Class 12 Tuition ?

Find best Class 12 Tuition in your locality on UrbanPro.

Are you a Tutor or Training Institute?

Join UrbanPro Today to find students near you
X

Looking for Class 12 Tuition Classes?

Find best tutors for Class 12 Tuition Classes by posting a requirement.

  • Post a learning requirement
  • Get customized responses
  • Compare and select the best
Post your learning requirement

Looking for Class 12 Tuition Classes?

Find best Class 12 Tuition Classes in your locality on UrbanPro

Post your learning requirement
    UrbanPro

UrbanPro.com is India's largest network of most trusted tutors and institutes. Over 25 lakh students rely on UrbanPro.com, to fulfill their learning requirements across 1,000+ categories. Using UrbanPro.com, parents, and students can compare multiple Tutors and Institutes and choose the one that best suits their requirements. More than 6.5 lakh verified Tutors and Institutes are helping millions of students every day and growing their tutoring business on UrbanPro.com. Whether you are looking for a tutor to learn mathematics, a German language trainer to brush up your German language skills or an institute to upgrade your IT skills, we have got the best selection of Tutors and Training Institutes for you. Read more

ThinkVidya Learning Pvt Ltd © 2010-2020All Rights Reserved