![SOLVED:(a) Use the Mean-Value Theorem to show that √(y)-√(x)<(y-x)/(2 √(x)) if 0< x <y. (b) Use the result in part (a) to show that if 0<x<y, then √(x y)<(1)/(2)(x+y). SOLVED:(a) Use the Mean-Value Theorem to show that √(y)-√(x)<(y-x)/(2 √(x)) if 0< x <y. (b) Use the result in part (a) to show that if 0<x<y, then √(x y)<(1)/(2)(x+y).](https://cdn.numerade.com/previews/0dd529dc-e417-4a0b-87a7-14a22269ce6c_large.jpg)
SOLVED:(a) Use the Mean-Value Theorem to show that √(y)-√(x)<(y-x)/(2 √(x)) if 0< x <y. (b) Use the result in part (a) to show that if 0<x<y, then √(x y)<(1)/(2)(x+y).
![definite integrals - The region between curves $y= {\sqrt x}$ , $0≤x≤4,y=1,x=4$ is revolved about $y=1$. Find the volume of a generated solid. - Mathematics Stack Exchange definite integrals - The region between curves $y= {\sqrt x}$ , $0≤x≤4,y=1,x=4$ is revolved about $y=1$. Find the volume of a generated solid. - Mathematics Stack Exchange](https://i.stack.imgur.com/v1Gpt.png)
definite integrals - The region between curves $y= {\sqrt x}$ , $0≤x≤4,y=1,x=4$ is revolved about $y=1$. Find the volume of a generated solid. - Mathematics Stack Exchange
![How do you find the volume of region bounded by graphs of y = x^2 and y = sqrt x about the x-axis? | Socratic How do you find the volume of region bounded by graphs of y = x^2 and y = sqrt x about the x-axis? | Socratic](https://useruploads.socratic.org/LjQCA6EsSavRxUg8TYzL_volume%20of%20x%5E2%20and%20rootx%29.png)
How do you find the volume of region bounded by graphs of y = x^2 and y = sqrt x about the x-axis? | Socratic
![sqrt(x*x+y*y)+3*cos(sqrt(x*x+y*y))+5 – Google Search has webGL charts « Adafruit Industries – Makers, hackers, artists, designers and engineers! sqrt(x*x+y*y)+3*cos(sqrt(x*x+y*y))+5 – Google Search has webGL charts « Adafruit Industries – Makers, hackers, artists, designers and engineers!](https://cdn-blog.adafruit.com/uploads/2012/03/pt_836.jpg)
sqrt(x*x+y*y)+3*cos(sqrt(x*x+y*y))+5 – Google Search has webGL charts « Adafruit Industries – Makers, hackers, artists, designers and engineers!
![Find the volume of the solid obtained by rotating about the y-axis the region enclosed by the graphs x = \sqrt{\sin y}, x = 0, 0 \leq y \leq \pi . | Homework.Study.com Find the volume of the solid obtained by rotating about the y-axis the region enclosed by the graphs x = \sqrt{\sin y}, x = 0, 0 \leq y \leq \pi . | Homework.Study.com](https://homework.study.com/cimages/multimages/16/volume6418157924719350476.jpg)