Let \(f:(0,1) \rightarrow R\) be the functions defined as \(f(x)=\sqrt{n}\) if \(x \in\left[\fra....

Channel:
Subscribers:
445,000
Published on ● Video Link: https://www.youtube.com/watch?v=_51kzJ3k2g4



Duration: 10:45
1 views
0


Let \(f:(0,1) \rightarrow R\) be the functions defined as \(f(x)=\sqrt{n}\) if \(x \in\left[\frac{1}{n+1}, \frac{1}{n}\right)\) where \(n \in N\). Let \(g :(0,1) \rightarrow R\) be a function such that \(\int_{x^2}^x \sqrt{\frac{1-t}{t}}=d t<g(x)<2 \sqrt{x}\) for all \(x\) \(\in(0,1)\). Then \(\lim _{x \rightarrow 0} f(x) g(x)\)  📲PW App Link - https://bit.ly/YTAI_PWAP 🌐PW Website - https://www.pw.live




Other Videos By PW Solutions


2024-07-29If [.] represents the greatest integer function, then the value of \(\left|\int_0^{\sqrt{\frac{\....
2024-07-29Let&nbsp;f:R&rarr;R be defined as f(x)=e-xsinx. If&nbsp;F:[0,1]&rarr;R is a differentiable funct....
2024-07-29If &int;0&pi;5cosx1+cosxcos3x+cos2x+cos3xcos3xdx1+5cosx=k&pi;16, then&nbsp;k is equal to&nbsp; _....
2024-07-29If \(f: R \rightarrow R\) be a continuous function satisfying \(\int_0^{\pi / 2} f(\sin 2 x) \cd....
2024-07-29The value of \(\int_{-1}^1 x^2 e^{\left[x^3\right]} d x\), where \([t]\) denotes the greatest in....
2024-07-29Let \(f:[0, \infty) \rightarrow[0, \infty)\) be defined as \(f(x)=\int_0^x[y] d y\)where \([x]\)....
2024-07-29Let \(f(x)\) be a differentiable function defined on \([0,2]\) such that&nbsp;f'(x)=f'(2-x) for ....
2024-07-29If \(\int_0^{100 \pi} \frac{\sin ^2 x}{\left(\frac{x}{\pi}-\left[\frac{x}{\pi}\right]\right)} d ....
2024-07-29The value of the definite integral&nbsp;&int;&pi;/245&pi;/24dx1+tan2x3....
2024-07-29&int;05cos&pi;x-x2dx, where&nbsp;[t] denotes greatest integer less than or equal to t, is equal ....
2024-07-29Let \(f:(0,1) \rightarrow R\) be the functions defined as \(f(x)=\sqrt{n}\) if \(x \in\left[\fra....
2024-07-29The value of the integral&nbsp;&int;-&pi;/2&pi;/2dx1+exsin6x+cos6x is equal to&nbsp;....
2024-07-29The value of&nbsp;&int;0&pi;ecosxsinx1+cos2xecosx+e-cosxdx is equal to:....
2024-07-29The greatest integer less than or equal to \(\int_1^2 \log _2\left(x^3+1\right) d x+\int_1^{\log....
2024-07-29For positive integer \(n\), define\(f(n)=n+\frac{16+5 n-3 n^2}{4 n+3 n^2}+\frac{32+n-3 n^2}{8 n+....
2024-07-29If the function \(f(x)=\frac{\cos (\sin x)-\cos x}{x^4}\) is continuous at each point in its dom....
2024-07-29Let \(f(x)=\left[x^2-x\right]+|-x+[x]|\), where \(x \in R\) and \([t]\) denotes the greatest int....
2024-07-29Let \(f:(-2,2) \rightarrow R\) be defined by\[f(x)=\left\{\begin{array}{cc}x[x] &amp; ,-2&lt;x&l....
2024-07-29Let \(k\) and \(m\) be positive real numbers such that the function \(f(x)=\left\{\begin{array}{....
2024-07-29limn&rarr;&infin;212-213212-215⋯⋯212-212n+1is equal to....
2024-07-29Let \(f\) and \(g\) be two functions defined by\[f(x)=\left\{\begin{array}{cc}x+1, &amp; x&lt;0 ....