Between any two real roots of the equation e^x sin x = 1, the equation e^x co...

Aspire's Library

A Place for Latest Exam wise Questions, Videos, Previous Year Papers,
Study Stuff for MCA Examinations - NIMCET

Best NIMCET Coaching
Aspire Study
Online Classes, Classroom Classes
and More.

Question Id : 11530 | Context :NIMCET 2023

Between any two real roots of the equation $e^x sin x = 1$, the equation $e^x cos x = –1$ has

🎥 Video solution / Text Solution of this question is given below:

Given:

$ e^x \sin x = 1 $ has two real roots → say $ x_1 $ and $ x_2 $

Apply Rolle’s Theorem:

Since $ f(x) = e^x \sin x $ is continuous and differentiable, and $ f(x_1) = f(x_2) $, ⇒ There exists $ c \in (x_1, x_2) $ such that $ f'(c) = 0 $

Compute:

\[ f'(x) = e^x(\sin x + \cos x) = 0 \Rightarrow \tan x = -1 \] At this point, \[ e^x \cos x = -1 \]

\[ \boxed{\text{At least one root}} \]

Get MCA exam-wise questions, solutions, test series & updates instantly on your phone.

🚀 Install Now

Aspire Study Online Test Series,
Information About Examination,
Syllabus, Notification
and More.

Click Here to
View More

Aspire Study Online Test Series,
Information About Examination,
Syllabus, Notification
and More.

Ask Your Question or Put Your Review.

Please provide more information - at least 10 characters