All Courses
Get the App Signup / Login
Sign in Open App
JEE Exam  >  JEE Notes  >  Mathematics (Maths) Class 12  >  RD Sharma Class 12 Solutions - Tangents and Normals

RD Sharma Class 12 Solutions - Tangents and Normals | Mathematics (Maths) Class 12 - JEE PDF Download

Download, print and study this document offline
Please wait while the PDF view is loading
 Page 1


16. Tangents and Normals
Exercise 16.1
1 A. Question
Find the The Slopes of the tangent and the normal to the following curves at the indicated points :
 at x = 4
Answer
Given:
y =  at x = 4
First, we have to find  of given function, f(x),i.e, to find the derivative of f(x)
y = 
? y = (
? y = 
(x
n
) = n.x
n – 1
The Slope of the tangent is 
Since, x = 4
x = 4
 = 
x = 4
 = 
x = 4
 = 
x = 4
 = 3
The Slope of the tangent at x = 4 is 3
Page 2


16. Tangents and Normals
Exercise 16.1
1 A. Question
Find the The Slopes of the tangent and the normal to the following curves at the indicated points :
 at x = 4
Answer
Given:
y =  at x = 4
First, we have to find  of given function, f(x),i.e, to find the derivative of f(x)
y = 
? y = (
? y = 
(x
n
) = n.x
n – 1
The Slope of the tangent is 
Since, x = 4
x = 4
 = 
x = 4
 = 
x = 4
 = 
x = 4
 = 3
The Slope of the tangent at x = 4 is 3
? The Slope of the normal = 
? The Slope of the normal = 
? The Slope of the normal = 
1 B. Question
Find the The Slopes of the tangent and the normal to the following curves at the indicated points :
 at x = 9
Answer
Given:
y =  at x = 9
First, we have to find  of given function, f(x),i.e, to find the derivative of f(x)
? y = 
? y = (
(x
n
) = n.x
n – 1
The Slope of the tangent is 
? y = (
Since, x = 9
x = 9
 = 
x = 9
 = 
x = 9
 = 
x = 9
 = 
x = 9
 = 
The Slope of the tangent at x = 9 is 
? The Slope of the normal = 
? The Slope of the normal = 
Page 3


16. Tangents and Normals
Exercise 16.1
1 A. Question
Find the The Slopes of the tangent and the normal to the following curves at the indicated points :
 at x = 4
Answer
Given:
y =  at x = 4
First, we have to find  of given function, f(x),i.e, to find the derivative of f(x)
y = 
? y = (
? y = 
(x
n
) = n.x
n – 1
The Slope of the tangent is 
Since, x = 4
x = 4
 = 
x = 4
 = 
x = 4
 = 
x = 4
 = 3
The Slope of the tangent at x = 4 is 3
? The Slope of the normal = 
? The Slope of the normal = 
? The Slope of the normal = 
1 B. Question
Find the The Slopes of the tangent and the normal to the following curves at the indicated points :
 at x = 9
Answer
Given:
y =  at x = 9
First, we have to find  of given function, f(x),i.e, to find the derivative of f(x)
? y = 
? y = (
(x
n
) = n.x
n – 1
The Slope of the tangent is 
? y = (
Since, x = 9
x = 9
 = 
x = 9
 = 
x = 9
 = 
x = 9
 = 
x = 9
 = 
The Slope of the tangent at x = 9 is 
? The Slope of the normal = 
? The Slope of the normal = 
? The Slope of the normal = 
? The Slope of the normal = – 6
1 C. Question
Find the The Slopes of the tangent and the normal to the following curves at the indicated points :
y = x
3
 – x at x = 2
Answer
Given:
y = x
3
 – x at x = 2
First, we have to find  of given function, f(x),i.e, to find the derivative of f(x)
(x
n
) = n.x
n – 1
The Slope of the tangent is 
? y = x
3
 – x
(x
3
) + 3 (x)
 = 3.x
3 – 1
 – 1.x
1 – 0
 = 3x
2
 – 1
Since, x = 2
x = 2
 = 3 (2)
2
 – 1
x = 2
 = (3 4) – 1
x = 2
 = 12 – 1
x = 2
 = 11
The Slope of the tangent at x = 2 is 11
? The Slope of the normal = 
? The Slope of the normal = 
? The Slope of the normal = 
1 D. Question
Find the The Slopes of the tangent and the normal to the following curves at the indicated points :
y = 2x
2
 + 3 sin x at x = 0
Answer
Given:
y = 2x
2
 + 3sinx at x = 0
Page 4


16. Tangents and Normals
Exercise 16.1
1 A. Question
Find the The Slopes of the tangent and the normal to the following curves at the indicated points :
 at x = 4
Answer
Given:
y =  at x = 4
First, we have to find  of given function, f(x),i.e, to find the derivative of f(x)
y = 
? y = (
? y = 
(x
n
) = n.x
n – 1
The Slope of the tangent is 
Since, x = 4
x = 4
 = 
x = 4
 = 
x = 4
 = 
x = 4
 = 3
The Slope of the tangent at x = 4 is 3
? The Slope of the normal = 
? The Slope of the normal = 
? The Slope of the normal = 
1 B. Question
Find the The Slopes of the tangent and the normal to the following curves at the indicated points :
 at x = 9
Answer
Given:
y =  at x = 9
First, we have to find  of given function, f(x),i.e, to find the derivative of f(x)
? y = 
? y = (
(x
n
) = n.x
n – 1
The Slope of the tangent is 
? y = (
Since, x = 9
x = 9
 = 
x = 9
 = 
x = 9
 = 
x = 9
 = 
x = 9
 = 
The Slope of the tangent at x = 9 is 
? The Slope of the normal = 
? The Slope of the normal = 
? The Slope of the normal = 
? The Slope of the normal = – 6
1 C. Question
Find the The Slopes of the tangent and the normal to the following curves at the indicated points :
y = x
3
 – x at x = 2
Answer
Given:
y = x
3
 – x at x = 2
First, we have to find  of given function, f(x),i.e, to find the derivative of f(x)
(x
n
) = n.x
n – 1
The Slope of the tangent is 
? y = x
3
 – x
(x
3
) + 3 (x)
 = 3.x
3 – 1
 – 1.x
1 – 0
 = 3x
2
 – 1
Since, x = 2
x = 2
 = 3 (2)
2
 – 1
x = 2
 = (3 4) – 1
x = 2
 = 12 – 1
x = 2
 = 11
The Slope of the tangent at x = 2 is 11
? The Slope of the normal = 
? The Slope of the normal = 
? The Slope of the normal = 
1 D. Question
Find the The Slopes of the tangent and the normal to the following curves at the indicated points :
y = 2x
2
 + 3 sin x at x = 0
Answer
Given:
y = 2x
2
 + 3sinx at x = 0
First, we have to find  of given function, f(x),i.e, to find the derivative of f(x)
(x
n
) = n.x
n – 1
The Slope of the tangent is 
? y = 2x
2
 + 3sinx
 
=
 2 (x
2
) + 3 (sinx)
 = 2 2x
2 – 1
 + 3 (cosx)
 (sinx) = cosx
 = 4x + 3cosx
Since, x = 2
? 
x = 0
 = 4 0 + 3cos(0)
cos(0) = 1
? 
x = 0
 = 0 + 3 1
? 
x = 0
 = 3
The Slope of the tangent at x = 0 is 3
? The Slope of the normal = 
? The Slope of the normal = 
? The Slope of the normal = 
1 E. Question
Find the The Slopes of the tangent and the normal to the following curves at the indicated points :
x = a (? – sin ?), y = a(1 + cos ?) at
? = – p/2
Answer
Given:
x = a( ) & y = a(1 + cos ) at 
Here, To find , we have to find  &  and and divide  and we get our desired .
(x
n
) = n.x
n – 1
? x = a( )
?  = a( ( ) – (sin ))
Page 5


16. Tangents and Normals
Exercise 16.1
1 A. Question
Find the The Slopes of the tangent and the normal to the following curves at the indicated points :
 at x = 4
Answer
Given:
y =  at x = 4
First, we have to find  of given function, f(x),i.e, to find the derivative of f(x)
y = 
? y = (
? y = 
(x
n
) = n.x
n – 1
The Slope of the tangent is 
Since, x = 4
x = 4
 = 
x = 4
 = 
x = 4
 = 
x = 4
 = 3
The Slope of the tangent at x = 4 is 3
? The Slope of the normal = 
? The Slope of the normal = 
? The Slope of the normal = 
1 B. Question
Find the The Slopes of the tangent and the normal to the following curves at the indicated points :
 at x = 9
Answer
Given:
y =  at x = 9
First, we have to find  of given function, f(x),i.e, to find the derivative of f(x)
? y = 
? y = (
(x
n
) = n.x
n – 1
The Slope of the tangent is 
? y = (
Since, x = 9
x = 9
 = 
x = 9
 = 
x = 9
 = 
x = 9
 = 
x = 9
 = 
The Slope of the tangent at x = 9 is 
? The Slope of the normal = 
? The Slope of the normal = 
? The Slope of the normal = 
? The Slope of the normal = – 6
1 C. Question
Find the The Slopes of the tangent and the normal to the following curves at the indicated points :
y = x
3
 – x at x = 2
Answer
Given:
y = x
3
 – x at x = 2
First, we have to find  of given function, f(x),i.e, to find the derivative of f(x)
(x
n
) = n.x
n – 1
The Slope of the tangent is 
? y = x
3
 – x
(x
3
) + 3 (x)
 = 3.x
3 – 1
 – 1.x
1 – 0
 = 3x
2
 – 1
Since, x = 2
x = 2
 = 3 (2)
2
 – 1
x = 2
 = (3 4) – 1
x = 2
 = 12 – 1
x = 2
 = 11
The Slope of the tangent at x = 2 is 11
? The Slope of the normal = 
? The Slope of the normal = 
? The Slope of the normal = 
1 D. Question
Find the The Slopes of the tangent and the normal to the following curves at the indicated points :
y = 2x
2
 + 3 sin x at x = 0
Answer
Given:
y = 2x
2
 + 3sinx at x = 0
First, we have to find  of given function, f(x),i.e, to find the derivative of f(x)
(x
n
) = n.x
n – 1
The Slope of the tangent is 
? y = 2x
2
 + 3sinx
 
=
 2 (x
2
) + 3 (sinx)
 = 2 2x
2 – 1
 + 3 (cosx)
 (sinx) = cosx
 = 4x + 3cosx
Since, x = 2
? 
x = 0
 = 4 0 + 3cos(0)
cos(0) = 1
? 
x = 0
 = 0 + 3 1
? 
x = 0
 = 3
The Slope of the tangent at x = 0 is 3
? The Slope of the normal = 
? The Slope of the normal = 
? The Slope of the normal = 
1 E. Question
Find the The Slopes of the tangent and the normal to the following curves at the indicated points :
x = a (? – sin ?), y = a(1 + cos ?) at
? = – p/2
Answer
Given:
x = a( ) & y = a(1 + cos ) at 
Here, To find , we have to find  &  and and divide  and we get our desired .
(x
n
) = n.x
n – 1
? x = a( )
?  = a( ( ) – (sin ))
?  = a(1 – ) ...(1)
 (sinx) = cosx
? y = a(1 + cos )
?  = a( ( ) + (cos ))
 (cosx) = – sinx
 (Constant) = 0
?  = a( + ( – sin ))
?  = a( – sin )
?  = – asin ...(2)
? 
? 
The Slope of the tangent is 
Since, 
? 
sin( ) = 1
cos( ) = 0
? 
? 
?  = 1
The Slope of the tangent at x = is 1
? The Slope of the normal = 
? The Slope of the normal = 
? The Slope of the normal = 
? The Slope of the normal = – 1
1 F. Question
Read More
204 videos|290 docs|139 tests
Join Course for Free

Top Courses for JEE

Related Exams
About this Document
Dec 22, 2024 Last updated
Document Description: RD Sharma Class 12 Solutions - Tangents and Normals for JEE 2024 is part of Mathematics (Maths) Class 12 preparation. The notes and questions for RD Sharma Class 12 Solutions - Tangents and Normals have been prepared according to the JEE exam syllabus. Information about RD Sharma Class 12 Solutions - Tangents and Normals covers topics like and RD Sharma Class 12 Solutions - Tangents and Normals Example, for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for RD Sharma Class 12 Solutions - Tangents and Normals.
Introduction of RD Sharma Class 12 Solutions - Tangents and Normals in English is available as part of our Mathematics (Maths) Class 12 for JEE & RD Sharma Class 12 Solutions - Tangents and Normals in Hindi for Mathematics (Maths) Class 12 course. Download more important topics related with notes, lectures and mock test series for JEE Exam by signing up for free. JEE: RD Sharma Class 12 Solutions - Tangents and Normals | Mathematics (Maths) Class 12 - JEE
Description
Full syllabus notes, lecture & questions for RD Sharma Class 12 Solutions - Tangents and Normals | Mathematics (Maths) Class 12 - JEE - JEE | Plus excerises question with solution to help you revise complete syllabus for Mathematics (Maths) Class 12 | Best notes, free PDF download
Information about RD Sharma Class 12 Solutions - Tangents and Normals
In this doc you can find the meaning of RD Sharma Class 12 Solutions - Tangents and Normals defined & explained in the simplest way possible. Besides explaining types of RD Sharma Class 12 Solutions - Tangents and Normals theory, EduRev gives you an ample number of questions to practice RD Sharma Class 12 Solutions - Tangents and Normals tests, examples and also practice JEE tests
204 videos|290 docs|139 tests
Join Course for Free
Download as PDF
Explore Courses for JEE exam

Top Courses for JEE

Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Related Searches

RD Sharma Class 12 Solutions - Tangents and Normals | Mathematics (Maths) Class 12 - JEE

,

Free

,

shortcuts and tricks

,

Sample Paper

,

Semester Notes

,

Extra Questions

,

RD Sharma Class 12 Solutions - Tangents and Normals | Mathematics (Maths) Class 12 - JEE

,

Objective type Questions

,

RD Sharma Class 12 Solutions - Tangents and Normals | Mathematics (Maths) Class 12 - JEE

,

Important questions

,

ppt

,

Viva Questions

,

past year papers

,

practice quizzes

,

mock tests for examination

,

Previous Year Questions with Solutions

,

Exam

,

pdf

,

video lectures

,

MCQs

,

Summary

,

study material

;
Additional Information about RD Sharma Class 12 Solutions - Tangents and Normals for JEE Preparation

RD Sharma Class 12 Solutions - Tangents and Normals Free PDF Download

The RD Sharma Class 12 Solutions - Tangents and Normals is an invaluable resource that delves deep into the core of the JEE exam. These study notes are curated by experts and cover all the essential topics and concepts, making your preparation more efficient and effective. With the help of these notes, you can grasp complex subjects quickly, revise important points easily, and reinforce your understanding of key concepts. The study notes are presented in a concise and easy-to-understand manner, allowing you to optimize your learning process. Whether you're looking for best-recommended books, sample papers, study material, or toppers' notes, this PDF has got you covered. Download the RD Sharma Class 12 Solutions - Tangents and Normals now and kickstart your journey towards success in the JEE exam.

Importance of RD Sharma Class 12 Solutions - Tangents and Normals

The importance of RD Sharma Class 12 Solutions - Tangents and Normals cannot be overstated, especially for JEE aspirants. This document holds the key to success in the JEE exam. It offers a detailed understanding of the concept, providing invaluable insights into the topic. By knowing the concepts well in advance, students can plan their preparation effectively. Utilize this indispensable guide for a well-rounded preparation and achieve your desired results.

RD Sharma Class 12 Solutions - Tangents and Normals Notes

RD Sharma Class 12 Solutions - Tangents and Normals Notes offer in-depth insights into the specific topic to help you master it with ease. This comprehensive document covers all aspects related to RD Sharma Class 12 Solutions - Tangents and Normals. It includes detailed information about the exam syllabus, recommended books, and study materials for a well-rounded preparation. Practice papers and question papers enable you to assess your progress effectively. Additionally, the paper analysis provides valuable tips for tackling the exam strategically. Access to Toppers' notes gives you an edge in understanding complex concepts. Whether you're a beginner or aiming for advanced proficiency, RD Sharma Class 12 Solutions - Tangents and Normals Notes on EduRev are your ultimate resource for success.

RD Sharma Class 12 Solutions - Tangents and Normals JEE Questions

The "RD Sharma Class 12 Solutions - Tangents and Normals JEE Questions" guide is a valuable resource for all aspiring students preparing for the JEE exam. It focuses on providing a wide range of practice questions to help students gauge their understanding of the exam topics. These questions cover the entire syllabus, ensuring comprehensive preparation. The guide includes previous years' question papers for students to familiarize themselves with the exam's format and difficulty level. Additionally, it offers subject-specific question banks, allowing students to focus on weak areas and improve their performance.

Study RD Sharma Class 12 Solutions - Tangents and Normals on the App

Students of JEE can study RD Sharma Class 12 Solutions - Tangents and Normals alongwith tests & analysis from the EduRev app, which will help them while preparing for their exam. Apart from the RD Sharma Class 12 Solutions - Tangents and Normals, students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc. The EduRev App will make your learning easier as you can access it from anywhere you want. The content of RD Sharma Class 12 Solutions - Tangents and Normals is prepared as per the latest JEE syllabus.
© EduRev
Education Revolution
Signup to see your scores go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup