UrbanPro
Login Ask & Answer Success Stories Paid Courses Free Classes 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

✕

Take Class 12 Tuition from the Best Tutors

  • Affordable fees
  • 1-1 or Group class
  • Flexible Timings
  • Verified Tutors

Book a Free Demo

Class 12 Tuition > Learn Class XI-XII Tuition (PUC) > differination of |x| in conditions
✕

Search in

differination of |x| in conditions

Asked by Last Modified  

27 Answers

Learn Class XI-XII Tuition (PUC)

Follow 0
Answer

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

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

"Decoding the World of Physics and Math: 12 Years of Expertise, Powered by a Teaching Enthusiasts"

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

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

IIT/BITSAT Decoded !!

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

Tutor

if x>0 it will be 1 and if x<0 then x=-1
Comments
Dislike Bookmark

Take positive and negative sign and than differentiate and is 1 and -1 if x>0and x<0.
Comments
Dislike Bookmark

Trainer

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

If x>=0, Then d|x|/d|y|=1 or else -1
Comments
Dislike Bookmark

All that glitter is not gold

1 or -1
Comments
Dislike Bookmark

View 25 more Answers

Related Questions

Why the negative end of the spindle fibre is directed towards the pole during Metaphase stage of Cell Division?
There is a pulling force of chromosomes towards the opposite end of the cell for the transition of metaphase to anaphase..
Abdur Rahman W.
3 0
6
Where is ISC 11th and 12th best coaching centre in Bangalore?
Better if you give some specific place in Bengaluru- so we can suggest you some best coaching center out there.
Kushal
1 0
7
What is stationary waves?
A wave appears to be stationary if the medium is moving in the opposite direction to that of the wave. Examples can be seen in river surfing. Or it can arise in a stationary medium as a result of interference...
Ravi Ranjan
how one can score good marks in every subject? how one can make subject easy
Hi dear, To make your study easy, one best way is to prepare notes of the subject u r studying. Instead of making elaborative notes prepare key points of the topics while studying and for processes or...
Sushmitha
What is Angular JS?
AngularJS, commonly referred to as Angular, is an open-source web application framework maintained and a community of individual developers and corporations to address many of the challenges encountered...
Anaveerappa
0 0
8

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

Ask a Question

Related Lessons

How To Prepare For Any Exam?
1. Prepare mentally yourself to give an exam. 2. Know the benifit of passing the exam it encourages you to do your best. 3. Never think about failure. 4. Be confident. 5. Watch and solve old papers. 6....
M

Mohit S.

1 0
0
What is the Chart of Accounts ?
The chart of accounts is a listing of the general ledger accounts to which amounts can be posted. The chart of accounts is a helpful tool for identifying the best account for recording a transaction. In...

Dev Group

1 0
1
Some formulas of algebra
Algebra: 1. (a + b) = a + 2ab + b 2. (a – b) = a – 2ab + b 3. (a + b) (a – b) = a – b 4. (x + a)(x + b) = x + (a + b)x + ab 5. (x + a)(x – b) = x + (a – b)x –...
K

Kanchan

2 0
0
For IIT - Pmt Aspirants: Trick To Learn - Directive Influence Of Substituents On Benzene (Learn Easily Through a Table).
The following table illustrates the directive inflence of various functional groups over benzene for second substitution. Learn easily through a table. VERY STRONG(ACTIVATING) PHENOXIDE ION...

Nidhi T.

0 0
0
Rules of debit and credit
Personal account: Debit the receiver and credit the giverReal account: Debit what comes in and credit what goes outNominal account: Debit all expenses & losses and credit all incomes & gains

Pankaj Agarwal

1 0
0

Recommended Articles

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 Mohammad Wazid, a skilled trainer for...

Mohammad Wazid is a certified professional tutor for class 11 students. He has 6 years of teaching experience which he couples with an energetic attitude and a vision of making any subject easy for the students. Over the years he has developed skills with a capability of understanding the requirements of the students. This...

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 Sandhya R, a B.Sc tutor from Bangalore

Sandhya is a proactive educationalist. She conducts classes for CBSE, PUC, ICSE, I.B. and IGCSE. Having a 6-year experience in teaching, she connects with her students and provides tutoring as per their understanding. She mentors her students personally and strives them to achieve their goals with ease. Being an enthusiastic...

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 Kolkata
Class 12 Tuition in Mumbai
Class 12 Tuition in Chennai
Class 12 Tuition in Pune
Class 12 Tuition in Lucknow
Class 12 Tuition in Jaipur
Class 12 Tuition in Noida
Online Tuition Class 12

Looking for Class 12 Tuition ?

Learn from the Best Tutors on UrbanPro

Are you a Tutor or Training Institute?

Join UrbanPro Today to find students near you
X

Looking for Class 12 Tuition Classes?

The best tutors for Class 12 Tuition Classes are on UrbanPro

  • Select the best Tutor
  • Book & Attend a Free Demo
  • Pay and start Learning

Take Class 12 Tuition with the Best Tutors

The best Tutors for Class 12 Tuition Classes are on UrbanPro

This website uses cookies

We use cookies to improve user experience. Choose what cookies you allow us to use. You can read more about our Cookie Policy in our Privacy Policy

Accept All
Decline All

UrbanPro.com is India's largest network of most trusted tutors and institutes. Over 55 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 7.5 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 © 2010-2025 All Rights Reserved