CA Foundation Exam > CA Foundation Questions > Between any two real roots of the equationexs...
Start Learning for Free
Between any two real roots of the equation ex sin x = 1, the equation ex cos x = - 1 has
- a)Atleast one root
- b)Exactly one root
- c)Atmost one root
- d)No root
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
Between any two real roots of the equationexsin x = 1, the equationexc...
Most Upvoted Answer
Between any two real roots of the equationexsin x = 1, the equationexc...
Solution:
Let f(x) = exsinx - 1
Let g(x) = excosx + 1
Now, we need to prove that there is atleast one root of g(x) between any two roots of f(x).
Let a and b be two real roots of f(x).
Then, f(a) = exsina - 1 = 0 and f(b) = exsinb - 1 = 0
Also, f(x) is continuous on [a,b] and differentiable on (a,b) (as ex is differentiable everywhere).
Therefore, by Rolle's Theorem, there exists a c ∈ (a,b) such that f'(c) = 0
Now, f'(x) = ex(sin x + cos x)
So, f'(c) = ec(sincos(c) + coscos(c)) = ec cos(c)(sin(c) + 1)
But ec ≠ 0 (as e is a positive constant), so sin(c) + 1 = 0
Therefore, cos(c) ≠ 0 (as sin(c) = -1), which implies that g(c) = excos(c) + 1 ≠ 0
So, g(x) does not have a root at c.
Therefore, there exists a root of g(x) between a and b (as g(a) and g(b) have opposite signs).
Hence, the correct option is (A) - Atleast one root.
Attention CA Foundation Students!
To make sure you are not studying endlessly, EduRev has designed CA Foundation study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CA Foundation.
|
Explore Courses for CA Foundation exam
|
|
Similar CA Foundation Doubts
Top Courses for CA FoundationView all
Between any two real roots of the equationexsin x = 1, the equationexcos x = - 1 hasa)Atleast one rootb)Exactly one rootc)Atmost one rootd)No rootCorrect answer is option 'A'. Can you explain this answer?
Question Description
Between any two real roots of the equationexsin x = 1, the equationexcos x = - 1 hasa)Atleast one rootb)Exactly one rootc)Atmost one rootd)No rootCorrect answer is option 'A'. Can you explain this answer? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about Between any two real roots of the equationexsin x = 1, the equationexcos x = - 1 hasa)Atleast one rootb)Exactly one rootc)Atmost one rootd)No rootCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Between any two real roots of the equationexsin x = 1, the equationexcos x = - 1 hasa)Atleast one rootb)Exactly one rootc)Atmost one rootd)No rootCorrect answer is option 'A'. Can you explain this answer?.
Between any two real roots of the equationexsin x = 1, the equationexcos x = - 1 hasa)Atleast one rootb)Exactly one rootc)Atmost one rootd)No rootCorrect answer is option 'A'. Can you explain this answer? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about Between any two real roots of the equationexsin x = 1, the equationexcos x = - 1 hasa)Atleast one rootb)Exactly one rootc)Atmost one rootd)No rootCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Between any two real roots of the equationexsin x = 1, the equationexcos x = - 1 hasa)Atleast one rootb)Exactly one rootc)Atmost one rootd)No rootCorrect answer is option 'A'. Can you explain this answer?.
Solutions for Between any two real roots of the equationexsin x = 1, the equationexcos x = - 1 hasa)Atleast one rootb)Exactly one rootc)Atmost one rootd)No rootCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for CA Foundation.
Download more important topics, notes, lectures and mock test series for CA Foundation Exam by signing up for free.
Here you can find the meaning of Between any two real roots of the equationexsin x = 1, the equationexcos x = - 1 hasa)Atleast one rootb)Exactly one rootc)Atmost one rootd)No rootCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Between any two real roots of the equationexsin x = 1, the equationexcos x = - 1 hasa)Atleast one rootb)Exactly one rootc)Atmost one rootd)No rootCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for Between any two real roots of the equationexsin x = 1, the equationexcos x = - 1 hasa)Atleast one rootb)Exactly one rootc)Atmost one rootd)No rootCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of Between any two real roots of the equationexsin x = 1, the equationexcos x = - 1 hasa)Atleast one rootb)Exactly one rootc)Atmost one rootd)No rootCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Between any two real roots of the equationexsin x = 1, the equationexcos x = - 1 hasa)Atleast one rootb)Exactly one rootc)Atmost one rootd)No rootCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice CA Foundation tests.
|
|
Explore Courses for CA Foundation exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup