Find the approximate value of (17/81)^(1/4) using differentiation.

Asked by Last Modified  

23 Answers

Follow 3
Answer

Please enter your answer

question is will you evaluate (97/81)^(1/4) in the same manner?
Comments
Dislike Bookmark

question is will you evaluate (97/81)^(1/4) in the same manner?
Comments
Dislike Bookmark

Tutor

Let y = f(x) = x^(1/4) To find: Approximate value of f(17/81) using differentiation We know that, f (x + delta x) = f(x) + .....using first principle 1st degree approximation. Here 'delta x' is the increment in x. Let us choose x such that f(x) is a rational number. If, x = 16/81 f(16/81)...
read more
Let y = f(x) = x^(1/4) To find: Approximate value of f(17/81) using differentiation We know that, f (x + delta x) = f(x) + [f'(x)* (delta x)].....using first principle 1st degree approximation. Here 'delta x' is the increment in x. Let us choose x such that f(x) is a rational number. If, x = 16/81 f(16/81) = 2/3 Therefore, delta x = (17/81)-(16/81) = 1/81 And f'(x) = d(x^(1/4))/dx = (1/4)* [x^ (-3/4)] So, approx. f(17/81) = f(16/81) + [(1/4)* {(16/81)^(-3/4)}] * (1/81) = (2/3) + (1/4) * (27/8) * (1/81) = (2/3) + (1/96) = 65/96 = 0.677 This is the approx value of (17/81)^(1/4) read less
Comments
Dislike Bookmark

Question is will you evaluate (97/81)^(1/4) in the same manner?
Comments
Dislike Bookmark

question is will you evaluate (97/81)^(1/4) in the same manner
Comments
Dislike Bookmark

question is will you evaluate (97/81)^(1/4) in the same manner .
Comments
Dislike Bookmark

Best Institute For Competitive Exams

65/96 is the answer. (16/81)^(1/4) = 2/3 which is useful to check your answer
Comments
Dislike Bookmark

Best Institute For Competitive Exams

Let y = f (x) = x^(1/4). Now differentiate to find delta y in terms of delta x and then find y at the given point. Realise that (16/81)^(1/4) = 2/3. On solving you will get 65/96.
Comments
Dislike Bookmark

(17/81)^1/4 = (17)^1/4/(81)^1/4 =(17)^1/4/3 Let f(x)= x^1/4 f'(x)=1/4x^3/4 {f(x+∆x)-f(x)}= f'(x)*∆x {f(x+∆x)-f(x)}=1/4x^3/4*∆x Write 17=16+1 then put x=16 abd ∆x=1 {f(16+1)-f(16)}=1/4(16)^3/4*1 f(17)-f(16)=1/4*2^4 f(17)=1/32 + f(16) f(17) = 1/32 + (16)^1/4 f(17) = 0.03125 + 2 (17)^1/4 = 2.03125 Approximate...
read more
(17/81)^1/4 = (17)^1/4/(81)^1/4 =(17)^1/4/3 Let f(x)= x^1/4 f'(x)=1/4x^3/4 {f(x+∆x)-f(x)}= f'(x)*∆x {f(x+∆x)-f(x)}=1/4x^3/4*∆x Write 17=16+1 then put x=16 abd ∆x=1 {f(16+1)-f(16)}=1/4(16)^3/4*1 f(17)-f(16)=1/4*2^4 f(17)=1/32 + f(16) f(17) = 1/32 + (16)^1/4 f(17) = 0.03125 + 2 (17)^1/4 = 2.03125 Approximate value of (17/81)^1/4 = 2.03125/3 = 0.677 read less
Comments
Dislike Bookmark

question is will you evaluate (97/81)^(1/4) in the same manner
Comments
Dislike Bookmark

View 21 more Answers

Related Questions

what is psueodo force?
The physically apparent but non-existent force needed by an observer in a non-inertial frame to make Newton's laws of motion hold true.
Yuvraj
Should I join JEE coaching in class 11?
If u have interested then join autherwise do not join.
Yash
0 0
View Comments5
How should I study Class 12 mathematics without coaching?
Solve R. D SHARMA (REFERENCE BOOK) FROM BASIC LEVEL TO HIGHER LEVEL. And YOU MUST TAKE HELP FROM YOUR SCHOOL MATHS TEACHER.
My
0 0
View Comments7
Can anyone suggest good IIT JEE Chemistry books?
Organic Chemistry
Sunita
Is it possible to get full marks in maths on class 12 CBSE without tution or coaching?
Yes, of course Many candidates perform self study
Samit
0 0
View Comments5

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

Ask a Question

Related Lessons

Kinematics: I.E. Irodov (Problems in General Physics) Problem 1.1
Let us solve Irodov problem 1.1 on Kinematics. The problem states: A motorboat going downstream overcame a raft at a point A; τ=60 min later it turned back and after sometime passed the raft...

Ashani Ray

0 0
View Comments0
Class 12 Boards: 4 Tips and more to crack the Physics Paper
Tip #1 From the NCERT book, practice each and every worked-out example, graph and diagram, especially- a) Ray diagram for Astronomical Telescope, Compound Microscope and Reflecting Telescope. b) Diagrams...

Akhil Goyal

0 0
View Comments0
Work, Energy and Power

Vishesh N.

0 0
View Comments0
Inclined Plane

Vishesh N.

0 0
View Comments0
Rotation

Vishesh N.

0 0
View Comments0

Recommended Articles

Get an Expert’s Guide and Tips to Make it...

An exclusive interview with Dr. Ashok Gopalakrishnan, CEO, Magnificient2 Software Services & Technology Inc. on approaching the JEE exam and how to make it to one of the IITs. Flexiguru.com: Flexiguru.com is an e-learning company offering flexible learning solutions that enhance teaching and learning. Launched with...

Read full article >

The IIT Dream: Ways to Make it True

The students who dream or make into IITs can be categorized into two -- Some planning at a very early stage and some starting at a much later stage after their first Board/Public exam. The difference may not be pronounced but the early starters have a slight edge over the latter. The competition for the elite IITs...

Read full article >

JEE Exam: Preparation Tips for Mathematics Paper

JEE (previously known as IIT JEE) is an engineering entrance exam conducted by Central Board of Secondary Education. To crack the JEE exam, students need to focus equally in all the three subjects -- Physics, Chemistry and Mathematics. One of the most critical and dreaded subjects in the JEE Syllabus is the Mathematics...

Read full article >

Why You Should Switch to Online Coaching...

Looking forward to become an IITian? Searching for best coaching mode to prepare for IIT JEE exam? Then look no further than IIT JEE online coaching classes and start preparing for the test anywhere anytime, as per your convenience. With better connectivity provisions in India, now more and more students are connected...

Read full article >

Find IIT JEE Coaching near you
IIT JEE Coaching in Mumbai
IIT JEE Coaching in Delhi
IIT JEE Coaching in Bangalore
IIT JEE Coaching in Kolkata
IIT JEE Coaching in Hyderabad
IIT JEE Coaching in Chennai
IIT JEE Coaching in Pune
IIT JEE Coaching in Jaipur
IIT JEE Coaching in Lucknow
IIT JEE Coaching in Gurgaon
Online IIT JEE Coaching

Looking for IIT JEE Coaching ?

Learn from the Best Tutors on UrbanPro

Are you a Tutor or Training Institute?

Join UrbanPro Today to find students near you