Let \( f \) be a real valued function with \( (n+1) \) derivatives at each point of \( R \). For...

Channel:
PW Solutions
Subscribers:
445,000
Published on ● Video Link: https://www.youtube.com/watch?v=cQgDFHjKktA


Duration: 4:10
24 views
0

Let \( f \) be a real valued function with \( (n+1) \) derivatives at each point of \( R \). For each pair of real numbers \( a, b, ab \), such that
\[
\ln \left[\frac{f(b)+f^{\prime}(b)+\ldots \ldots+f^{(n)}(b)}{f(a)+f^{\prime}(a)+\ldots \ldots+f^{(n)}(a)}\right]=b-a
\]
Statement-1 : There is a number \( c \in(a, b) \) for which \( f^{(n+1)}(c)=f(c) \)
because
Statement-2 : If \( h(x) \) be a derivable function such that \( h(p)=h(q) \) then by Rolle's theorem \( h^{\prime}(d)=0 ; d \in(p, q) \)
(a) Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1
(b) Statement-1 is true, statement-2 is true and statement-2 is not correct explanation for statement-1
(c) Statement-1 is true, statement-2 is false
(d) Statement-1 is false, statement-2 is true
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live



Other Videos By PW Solutions


2022-10-28An acid-base indicator has \( K_{\mathrm{HIn}}=3.0 \times 10^{-5} \). The acid form of the indic...
2022-10-28In which of the following cases is the solution of \( \mathrm{AgCl} \) unsaturated? (a) \( \left...
2022-10-28If \( (f(x)-1)\left(x^{2}+x+1\right)^{2}-(f(x)+1)\left(x^{4}+x^{2}+1\right)=0 \) \( \forall x \i...
2022-10-28Let \( f(x)=1+\int_{0}^{1}\left(x e^{y}+y e^{x}\right) f(y) d y \) where \( x \) and \( y \) are...
2022-10-28Common tangent(s) to \( y=x^{3} \) and \( x=y^{3} \) is/are : (a) \( x-y=\frac{1}{\sqrt{3}} \) (...
2022-10-28For the equation \( \frac{e^{-x}}{1+x}=\lambda \) which of the following statement(s) is/are cor...
2022-10-28Consider \( f(x)=\sin ^{5} x+\cos ^{5} x-1, x \in\left[0, \frac{\pi}{2}\right] \), which of the ...
2022-10-28Let \( f(x) \) be twice differentiable function such that \( f^{\prime \prime}(x)0 \) in \( [0,2...
2022-10-28Let \( f:[-3,4] \rightarrow R \) such that \( f^{\prime \prime}(x)0 \) for all \( x \in[-3,4] \)...
2022-10-28Let a function \( f(x)=[x]\{x\}-|x| \) where [.], \( \{\cdot\} \) are greatest integer and fract...
2022-10-28Let \( f \) be a real valued function with \( (n+1) \) derivatives at each point of \( R \). For...
2022-10-28Let \( f(x)=\left\{\begin{array}{cc}x[x] & 0 \leq x2 \\ (x-1)[x] & 2 \leq x \leq 3\end{array}\ri...
2022-10-28If \( f(x)=\frac{(x-1)(x-2)}{(x-3)(x-4)} \), then number of local extremas for \( g(x) \), where...
2022-10-28Let \( f(x)=\left\{\begin{array}{cc}x[x] & 0 \leq x2 \\ (x-1)[x] & 2 \leq x \leq 3\end{array}\ri...
2022-10-28Define : \( f(x)=\left|x^{2}-4 x+3\right| \ln x+2(x-2)^{1 / 3}, x0 \) \[ h(x)=\left\{\begin{arra...
2022-10-28Define : \( f(x)=\left|x^{2}-4 x+3\right| \ln x+2(x-2)^{1 / 3}, x0 \) \[ h(x)=\left\{\begin{arra...
2022-10-28Let \( f(x)=\lim _{n \rightarrow \infty} n^{2} \tan \left(\ln \left(\sec \frac{x}{n}\right)\righ...
2022-10-28If \( f(x)=\left(\frac{x}{2}\right)-1 \), then on the interval \( [0, \pi] \) : (a) \( \tan (f(x...
2022-10-28The function \( f(x)=\left[\sqrt{1-\sqrt{1-x^{2}}}\right] \), (where [.] denotes greatest intege...
2022-10-28If \( f(x)=\left[\begin{array}{l}\frac{\sin \left[x^{2}\right] \pi}{x^{2}-3 x+8}+a x^{3}+b ; 0 \...
2022-10-28If \( y=f(x) \) is differentiable \( \forall x \in R \), then (a) \( y=|f(x)| \) is differentiab...


Tags:
pw