Consider \( f, g \) and \( h \) be three real valued functions defined on \( R \). Let \( f(x)=\...

Channel:
Subscribers:
449,000
Published on ● Video Link: https://www.youtube.com/watch?v=CGUW87aiZ9k



Duration: 9:17
1 views
0


Consider \( f, g \) and \( h \) be three real valued functions defined on \( R \).
Let \( f(x)=\left\{\begin{aligned}-1, & x0 \\ 0, & x=0, g(x)=x\left(1-x^{2}\right) \text { and } h(x) \text { be such that } \\ 1, & x0 \end{aligned}\right. \) \( h^{\prime \prime}(x)=6 x-4 \)
Also, \( h(x) \) has local minimum value 5 at \( x=1 \).
The area bounded by \( y=h(x), y=g(f(x)) \) between \( x=0 \) and \( x=2 \) equals
(a) \( 23 / 2 \)
(b) \( 20 / 3 \)
(c) \( 32 / 3 \)
(d) \( 40 / 3 \)
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live




Other Videos By PW Solutions


2022-10-27The points \( A(4,5,10), B(2,3,4) \) and \( C(1,2,-1) \) are three vertices of a parallelogram \...
2022-10-27If the line \( \frac{x}{1}=\frac{y}{2}=\frac{z}{3} \) intersects the line \( 3 \beta^{2} x+3(1-2...
2022-10-27Let \( P(a, b, c) \) be any point on the plane \( 3 x+2 y+z=7 \), then find the least value of \...
2022-10-27Through a point \( P(h, k, l) \) a plane is drawn at right angles to \( O P \) to meet the coord...
2022-10-27Equation of the line through the point \( (1,1,1) \) and intersecting the lines \( 2 x-y-z-2=0=x...
2022-10-27Find the direction cosines of the resultant of the vectors \( (\hat{\mathbf{i}}+\hat{\mathbf{j}}...
2022-10-27In a regular tetrahedron, if the distance between the mid-points of opposite edges is unity, its...
2022-10-27The position vector of the point of intersection of three planes r. \( \mathbf{n}_{1}=q_{1} \), ...
2022-10-27If \( \left|x_{1}\right|\left|y_{1}\right|+\left|z_{1}\right|,\left|y_{2}\right|\left|x_{2}\righ...
2022-10-27In the figure, a vectors \( x \) satisfies the equation \( x-w=v \). Then, \( x \) is equal to (...
2022-10-27Consider \( f, g \) and \( h \) be three real valued functions defined on \( R \). Let \( f(x)=\...
2022-10-27A variable plane cutting coordinate axes in \( A, B, C \) is at a constant distance from the ori...
2022-10-27Let \( f(x) \) and \( g(x) \) be two continuous functions defined from \( R \rightarrow R \), su...
2022-10-27Let \( L=\lim _{x \rightarrow \infty}\left(x \log x+2 x \cdot \log \sin \left(\frac{1}{\sqrt{x}}...
2022-10-27Number of critical points of the function, \( f(x)=\frac{2}{3} \sqrt{x^{3}}-\frac{x}{2}+\int_{1}...
2022-10-27If \( f: D \rightarrow R, f(x)=\frac{x^{2}+b x+c}{x^{2}+b_{1} x+c_{1}} \), where \( \alpha, \bet...
2022-10-27Match the column. (B) If the value of \( \lim _{x \rightarrow 0^{+}}\left(\frac{(3 / x)+1}{(3 / ...
2022-10-27If \( \{(\alpha+1)(\beta-1)+(\beta+1)(\alpha-1)\} a+(\alpha-1)(\beta-1)=0 \) and \( a(\alpha+1)(...
2022-10-27Differentiate the following functions w.r.t. \( x \). \[ \left(x^{x}\right)^{x} \]
2022-10-27Let \( f \) be a differentiable function satisfying \[ [f(x)]^{n}=f(n x) \text { for all } x \in...
2022-10-27If \( x^{y}+y^{x}=2 \), then find \( \frac{d y}{d x} \).



Tags:
pw