Math, asked by sehrishiqbalsehrishi, 6 months ago

if f is a bounded function on sqare bracket [a,b] such that f(x)=0 except for xin {c1,c2,....,cn} in [a,b].show that U(f)=L(f)=0

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Answered by kings07

Change tx to tex
↓↓
$<!DOCTYPE html> <html lang="en"> <head> <title>CUBE</title> </head> <body> <div class="container"> <div id="cube"> <div class="front">kings07</div> <div class="back">#kings</div> <div class="right">kings</div> <div class="left">kings</div> <div class="top">kings</div> <div class="bottom">kings</div> </div> </div> <style> body { padding-left: 30%; padding-top: 5%; } .container { width: 200px; height: 200px; position: relative; -webkit-perspective: 1000px; -moz-perspective: 1000px; } #cube { width: 100%; height: 100%; position: absolute; -webkit-transform-style: preserve-3d; -webkit-animation: rotatecube 10s infinite; -moz-transform-style: preserve-3d; -moz-animation: rotatecube 10s infinite; } #cube div { width: 200px; height: 200px; display: block; position: absolute; border: none; line-height: 200px; text-align: center; font-size: 50px; font-weight: bold; } @-webkit-keyframes rotatecube { 0% { -webkit-transform: rotateX(0deg) rotateY(360deg) rotateZ(90deg); } 25% { -webkit-transform: rotateX(90deg) rotateY(270deg) rotateZ(180deg); } 50% { -webkit-transform: rotateX(180deg) rotateY(180deg) rotateZ(0deg); } 75% { -webkit-transform: rotateX(270deg) rotateY(90deg) rotateZ(360deg); } 100% { -webkit-transform: rotateX(360deg) rotateY(0deg) rotateZ(270deg); } } @-moz-keyframes rotatecube { 0% { -moz-transform: rotateX(0deg) rotateY(360deg) rotateZ(90deg); } 25% { -moz-transform: rotateX(90deg) rotateY(270deg) rotateZ(180deg); } 50% { -moz-transform: rotateX(180deg) rotateY(180deg) rotateZ(0deg); } 75% { -moz-transform: rotateX(270deg) rotateY(90deg) rotateZ(360deg); } 100% { -moz-transform: rotateX(360deg) rotateY(0deg) rotateZ(270deg); } } .front { background: rgba(255,0,0,.5); } .back { background: rgba(0,255,0,.5); } .right { background: rgba(0,0,255,.5); } .left { background: rgba(0,255,255,.5); } .top { background: rgba(255,0,255,.5); } .bottom { background: rgba(255,255,0,.5); } #cube .front { -webkit-transform: rotateY(0deg ) translateZ( 100px ); -moz-transform: rotateY( 0deg ) translateZ( 100px ); } #cube .back { -webkit-transform: rotateX( 180deg ) translateZ( 100px ); -moz-transform: rotateX( 180deg ) translateZ( 100px ); } #cube .right { -webkit-transform: rotateY( 90deg ) translateZ( 100px ); -moz-transform: rotateY( 90deg ) translateZ( 100px ); } #cube .left { -webkit-transform: rotateY( -90deg ) translateZ( 100px ); -moz-transform: rotateY( -90deg ) translateZ( 100px ); } #cube .top { -webkit-transform: rotateX( 90deg ) translateZ( 100px ); -moz-transform: rotateX( 90deg ) translateZ( 100px ); } #cube .bottom { -webkit-transform: rotateX( -90deg ) translateZ( 100px ); -moz-transform: rotateX( -90deg ) translateZ( 100px ); } </style> </body> </html>$ ......hru....✌✌✌✌✌✌✌

Answered by Anonymous

$<svg id="wrap" width="300" height="300">  <svg> <circle cx="150" cy="150" r="130" style="stroke: lightblue; stroke-width:18; fill:transparent"/> <circle cx="150" cy="150" r="115" style="fill:#2c3e50"/> <path style="stroke: #2c3e50; stroke-dasharray:820; stroke-dashoffset:820; stroke-width:18; fill:transparent" d="M150,150 m0,-130 a 130,130 0 0,1 0,260 a 130,130 0 0,1 0,-260"> <animate attributeName="stroke-dashoffset" dur="6s" to="-820" repeatCount="indefinite"/> </path> </svg>  <svg> <path id="hourglass" d="M150,150 C60,85 240,85 150,150 C60,215 240,215 150,150 Z" style="stroke: white; stroke-width:5; fill:white;" /> <path id="frame" d="M100,97 L200, 97 M100,203 L200,203 M110,97 L110,142 M110,158 L110,200 M190,97 L190,142 M190,158 L190,200 M110,150 L110,150 M190,150 L190,150" style="stroke:lightblue; stroke-width:6; stroke-linecap:round" /> <animateTransform xlink:href="#frame" attributeName="transform" type="rotate" begin="0s" dur="3s" values="0 150 150; 0 150 150; 180 150 150" keyTimes="0; 0.8; 1" repeatCount="indefinite" /> <animateTransform xlink:href="#hourglass" attributeName="transform" type="rotate" begin="0s" dur="3s" values="0 150 150; 0 150 150; 180 150 150" keyTimes="0; 0.8; 1" repeatCount="indefinite" /> </svg>  <svg>  <polygon id="upper" points="120,125 180,125 150,147" style="fill:#2c3e50;"> <animate attributeName="points" dur="3s" keyTimes="0; 0.8; 1" values="120,125 180,125 150,147; 150,150 150,150 150,150; 150,150 150,150 150,150" repeatCount="indefinite"/> </polygon>  <path id="line" stroke-linecap="round" stroke-dasharray="1,4" stroke-dashoffset="200.00" stroke="#2c3e50" stroke-width="2" d="M150,150 L150,198">  <animate attributeName="stroke-dashoffset" dur="3s" to="1.00" repeatCount="indefinite"/>  <animate attributeName="d" dur="5s" to="M150,195 L150,195" values="M150,150 L150,198; M150,150 L150,198; M150,198 L150,198; M150,195 L150,195" keyTimes="0; 0.65; 0.9; 1" repeatCount="indefinite"/>  <animate attributeName="stroke" dur="3s" keyTimes="0; 0.65; 0.8; 1" values="#2c3e50;#2c3e50;transparent;transparent" to="transparent" repeatCount="indefinite"/> </path>  <g id="lower"> <path d="M150,180 L180,190 A28,10 0 1,1 120,190 L150,180 Z" style="stroke: transparent; stroke-width:5; fill:#2c3e50;"> <animateTransform attributeName="transform" type="translate" keyTimes="0; 0.65; 1" values="0 15; 0 0; 0 0" dur="3s" repeatCount="indefinite" /> </path> <animateTransform xlink:href="#lower" attributeName="transform" type="rotate" begin="0s" dur="3s" values="0 150 150; 0 150 150; 180 150 150" keyTimes="0; 0.8; 1" repeatCount="indefinite"/> </g>  <path d="M150,150 C60,85 240,85 150,150 C60,215 240,215 150,150 Z" style="stroke: white; stroke-width:5; fill:transparent;"> <animateTransform attributeName="transform" type="rotate" begin="0s" dur="3s" values="0 150 150; 0 150 150; 180 150 150" keyTimes="0; 0.8; 1" repeatCount="indefinite"/> </path>  <path id="frame" d="M100,97 L200, 97 M100,203 L200,203" style="stroke:lightblue; stroke-width:6; stroke-linecap:round"> <animateTransform attributeName="transform" type="rotate" begin="0s" dur="3s" values="0 150 150; 0 150 150; 180 150 150" keyTimes="0; 0.8; 1" repeatCount="indefinite"/> </path> </svg> </svg>$

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if f is a bounded function on sqare bracket [a,b] such that f(x)=0 except for xin {c1,c2,....,cn} in [a,b].show that U(f)=L(f)=0​

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if f is a bounded function on sqare bracket [a,b] such that f(x)=0 except for xin {c1,c2,....,cn} in [a,b].show that U(f)=L(f)=0