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

What are the 3 Types of networks..?
They are as follows : LAN (local area network), MAN (metropolitan area network) and WAN (wide area network).
RAJESH N.
1 0
7
What equipments and applications required to start online tuitions
Skype, Gotomeeting.com, etc
Asha Krishnan B.s
X-rays are produced when an element of high atomic weight is bombarded by high energy __________. (Protons, Electrons, Neutrons, Photons
Electrons
Narendra Kumar
Using all the letters of the word "FRIDAY", how many different words can be formed?
Total letters in word FRIDAY are 6, so 6! ways letters can be arranged so total words formed are 6*5*4*3*2*1=720
Nilam
Which of the following usually is not a way to conserve water during a water shortage? 1. taking a shower instead of a bath 2. fixing leaky faucets 3. turning off the water while brushing your teeth 4. waiting until you have enough dishes to fill the dishwasher before running it
Option 1.
Sugantha
0 0
9

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

Ask a Question

Related Lessons

Statistics
Flash back from IX Class A systematic record of facts or different values of a quantity is called data. Features of the data Statistics deals with collection, presentation, analysis and interpretation...
A

Amrtha S.

0 0
0
How to overcome ORGANIC CHEMISTRY PHOBIA....for XI & XII JEE MAINS/NEET ASPIRANTS...
Students preparaing for NEET and JEE MAINS exam in particular loose marks particularly in simple topics in organic chemistry.One such topic is G.O.C.As G.O.C is a mix up all the basics student should have...

Jagan's Js Academy

2 0
0
English (Fill In The Blank)
Question: 1. Even after a century of ____________ investigation, the relation of the solar cycle to terrestrial weather remains _____________. A. Meticulous, apparent B. Cursory, clear C. Sedulous, pertinent...

Sujoy Das

0 0
0
Bills of exchange
Bills of exchange is a negotiable instrument. It is drawn by a creditor on the debtor and accepted by the debtor in writing for the amount owed by the debtor to settle it on a specific maturity date. Bills...

Vijayakumar V.

0 0
0
Class 11: Important Prefixes In The Si System
Mostly commonly terms like "picometre", "nanometre" needs to be converted to SI units to solve in one unit correctly. Micrometre, picometre, nanometre are often used. One can convert them in metres, etc (units).

Nidhi T.

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