.pf{position:relative;background-color:#fff;overflow:hidden;margin:0;border:0}.pc{position:absolute;border:0;padding:0;margin:0;top:0;left:0;width:100%;height:100%;overflow:hidden;display:block;transform-origin:0 0;-ms-transform-origin:0 0;-webkit-transform-origin:0 0}.bi{position:absolute;border:0;margin:0}.c{position:absolute;border:0;padding:0;margin:0;overflow:hidden;display:block}.t{position:absolute;white-space:pre;font-size:1px;transform-origin:0 100%;-ms-transform-origin:0 100%;-webkit-transform-origin:0 100%;unicode-bidi:bidi-override;-moz-font-feature-settings:"liga" 0}.t:after{content:''}.t:before{content:'';display:inline-block}.t span{position:relative;unicode-bidi:bidi-override}.pi{display:none}@media screen{.pf{margin:13px auto;box-shadow:1px 1px 3px 1px #333;border-collapse:separate}}.ff1{font-family:ff1;line-height:1.032000;font-style:normal;font-weight:400;visibility:visible}@font-face{font-family:ff2;src:url(data:application/font-woff;base64,d09GRgABAAAAAAWUAA8AAAAACCQAAQAAAAAAAAAAAAAAAAAAAAAAAAAAAABGRlRNAAAFeAAAABoAAAAcac4ucUdERUYAAAVcAAAAHAAAAB4AJwAMT1MvMgAAAcQAAAA+AAAAVmESZzpjbWFwAAACHAAAAEQAAAFCAA8G0GN2dCAAAANoAAAABgAAAAYFOwBEZnBnbQAAAmAAAAECAAABcwZZnDdnbHlmAAADgAAAAKkAAADAnGPfP2hlYWQAAAFYAAAALwAAADb6E0S/aGhlYQAAAYgAAAAbAAAAJAsABc5obXR4AAACBAAAABgAAAAYDZgA3mxvY2EAAANwAAAADgAAAA4AuACEbWF4cAAAAaQAAAAdAAAAIAITAEhuYW1lAAAELAAAAQUAAAIxnz3xlXBvc3QAAAU0AAAAKAAAADfGRp4GcHJlcAAAA2QAAAAEAAAABLgAACt4nGNgZGBgAOKJs5fzxPPbfGWQ52AAgVPr/yJoFwYGVlvWQ0AuBwMTSBQAJlgJ6wB4nGNgZGBgPcQABKzHwaQtAyMDKmADADFYAd4AeJxjYGRgYGBj4GBgYgABRjDJxQDi2oOYAAOhAF4AAAB4nGNgZJRlnMDAysDAasw6k4GBUQ5CM19nSGMSYmBgYmBlZoABRgYkEJDmmgKkFBgUWQ+B+BASogYAR9sHDwAAAuwARAAAAAACqgAAAAIAAAI5AAAFxwCaeJxjYGBgZoBgGQZGBhCwAfIYwXwWBgUgzQKEIL7i//9AUuH///+PoSoZGNkYYEwGRiYgwcSACoCSzCwMwxoAAGd9BuJ4nF2QPU7EMBCFxzgs5AZIFpItKxQrr+ipUjiRUJpAKDwNP9KuRPYOSGloXHCWoTNdLoZgko222MYz783o87MTgGsS5G34FuILk/j7TOCvfyAH+fK8SSCc1lXvSbyyOHNsrA130umaZFE/Bos66ni/jbrW729byoq58mAX8VYTdKHn8ykYKlEd2x3iHXOyiZPNnIhM2C+E/UxgwC8vnbtGk7xpw0OgwSsqPSpjdEVjG2j0yiDy1uqYlOtHf7VkvuDMqzU3lwdKF6hUBBjjQVlDQ4wq8jsWnWA8MQScGuVi8E9MRFlUSQztPBqsUZNhjTWcEz3fnbumCxUnNbj5ByTqa+QAALgAACsAKgBEBREAAAAAACwALAAsACwALABgAAB4nB2NPQrCQBSEZ39eNnbuDQwoFoLxp43a5ARCbpDCI0laS0HIVkvK9AEPkCt4gRiCby2Gb97Am4FEDsiSCigYbGuBNHNGi8+hjqjPnJJsUasQU4idieSYORHyo03sKrFJLhfTUtynGxXDM9cduBIVQCdq/70Xjzj10Kx47oE3K9zsVc+eaZiKOevR8AegNg23EHO3D0NrVqUffuyoHc5eX78v4Afm1DABAAAAeJytj8FqwkAURc9otBSkO6GLLrLWRpJsLC6zEJEiKCK2u9QOIRASiNE/6C/0c/pN/YTe1Fl2UWgHZubM5d557wED3jG0yzDk3nGHKzaOu0R8OPYYmjvHPQbm0XFf+pucxruWMvpOtdzhhsRxlxeeHXvyfDrucWtix31G5kmJFUvWbNkzZoGl4KyzIedASiBHJe0VktVyvd2PF7Y42yY/pEFSFZI3cmec5Emp9bTZqUgFc+VK/dPetRwWn5gJoe6Z9u8rX/yR0gFT7Vh/RDyoRFU286rOrB9PQn/m/9ih9CgOpkEcRor8fd6d3DVH+dv52r4uM7Gz9TGvSj9SL/9Q6AuCplwXAAAAeJxjYGIAg39zGVIZsAE2IGZkYGJgZmBhZOLwS8xN9U3VMwAAatsEr3icY2BkYGDgAWIxIGZiYARCViBmAfMYAAPVADR4nGNgYGBkAIIreSYFIPrU+r8MMBoARhUG1AAA) format("woff")}.ff2{font-family:ff2;line-height:.719727;font-style:normal;font-weight:400;visibility:visible}.m0{transform:matrix(.255207,0,0,.255207,0,0);-ms-transform:matrix(.255207,0,0,.255207,0,0);-webkit-transform:matrix(.255207,0,0,.255207,0,0)}.ls0{letter-spacing:0}.sc0{text-shadow:-.015em 0 transparent,0 .015em transparent,.015em 0 transparent,0 -.015em transparent}@media screen and (-webkit-min-device-pixel-ratio:0){.sc0{-webkit-text-stroke:.015em transparent;text-shadow:none}}.ws0{word-spacing:0}.fc0{color:#6e3636}.fs0{font-size:80.156074px}.y3{bottom:-190.096654px}.y2{bottom:-164.526132px}.y0{bottom:0}.y1{bottom:522.666667px}.h4{height:56.029096px}.h3{height:57.690456px}.h2{height:522.666667px}.h1{height:1045.32925px}.h0{height:1045.333333px}.w1{width:783.996938px}.w0{width:784px}.x0{left:0}.x1{left:76.61256px}

MATH 140 Lecture : derivatives - 3

Canada

Calculus 1

Mathematics & Statistics (Sci)

Mark Fels

McGill University

Introduction to the Engineering Profession

Linear Algebra and Geometry

General Chemistry 1

Mechanics and Waves

questiom <picture><source srcset="https://prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/21/2110711.webp" type="image/webp"></source><img src="https://prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/21/2110711.png" alt=""></picture> <div id="hn7" class="hidden">What is Nul A? Are the following subsets of R2 subspaces? If not, use a counter-example to show which condition is not satisfied.</div> Show transcribed image text What is Nul A? Are the following subsets of R2 subspaces? If not, use a counter-example to show which condition is not satisfied.

In example 4.1.2 we showed that <img src="data:image/png;base64,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" class="fm-editor-equation" data-mlang="latex" data-equation="int_%7B0%7D%5E%7B1%7D%5Cfrac%7B1%7D%7B3%7D">. Use this fact and properties of integral to evaluate<img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABYAAAAiBAMAAACpcTSzAAAACXBIWXMAAABkAAAAZAAPlsXdAAAAKlBMVEVHcEwAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAHrpZrAAAADXRSTlMAiGFEIpm33TN3zO4ReKM/kwAAAJdJREFUGNNjYIAApmAGBBDGxtYUgLNZMjbA2YwTGDgSHSBs9gaEPm8kM9SQ2IFI7CIEk+UGgs10AcFmXIBgcyUg2LwCCLatAYI99wCCHY5k1TIk9kUEk+MykrV3sFvLFoBgsysgOcEBwTZnYFGCsacyHGWBuS6JQZGhAMrewyDIAPEBM3MAkA2xopvVAa6GeQYDA6sn2AoAwJIV2qn82OoAAAAASUVORK5CYII=" class="fm-editor-equation" data-mlang="latex" data-equation="int_%7B0%7D%5E%7B1%7D%7B%7D">.

A Cubic Equation: Let <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAC0AAAAZBAMAAABX37oSAAAACXBIWXMAAABkAAAAZAAPlsXdAAAAJ1BMVEVHcEwAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAB+jSoGAAAADXRSTlMAiEQzEVV3u2b5IqHX6BcXEgAAALhJREFUKM9jYMAAMsePC2CKMrAaNCQwYAPMWgFYxbmZFLCKuzMJYBVPYyoAUU7o4g4MC4AkU1AFVl2cBpFYxVkd0rGKM7AUM4SmdRtgiFsIswRoMzowcAkCAdCFTkpKSlogiUgXBzEkdQuB0kIMDNYMlgoMxSDzQOoRIdPjoLk4ZAIHkAXUr4SwhtFkB9u2rVHINkJ8arSAwYAZWZiaPsUKLISxizNEOmATBfsUCwD6dAE2caBPGRgAhNodPfDLjlwAAAAASUVORK5CYII=" class="fm-editor-equation" data-mlang="latex" data-equation="3x%3D%5Cfrac%7Bpi%7D%7B3%7D">, and let <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADoAAAAJBAMAAACReyIYAAAACXBIWXMAAABkAAAAZAAPlsXdAAAAKlBMVEVHcEwAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAHrpZrAAAADnRSTlMAiEQzEXdmVaqZIue7zL5PPcgAAACuSURBVBjTY3CdzNzAAANsQkFsSWHMIToMDOWhGQYMDAmTWAUYuASBQICBYTWDqAYD78ICNgaWAg1GBwYGlw0cCnC9kgwMggw8wXtFGFgcRMGGCXAzMLCA9AbAZEWYZIASh0GyjAI2QFIJCAxAJrPrMHAvdOBgYC7ZwMZuwMA0qZEByVXFbEFijEFlDKxTp1dxCDAwezUjZBmYQYiFGegeA2YQX5dpAgNu4FaKRxIAM8UZC+wbGcYAAAAASUVORK5CYII=" class="fm-editor-equation" data-mlang="latex" data-equation="y%3Dcosx."> Use the result of Example<img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAcAAAAJBAMAAAAMdiuQAAAACXBIWXMAAABkAAAAZAAPlsXdAAAAIVBMVEUAAABHcEwAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACArOP1AAAACnRSTlNmAFUi6jOIu0QRpKBmLAAAADBJREFUCNdjEGAqEGAwE1QRYIiaKNXAIAhiCQoCxQTFGIGEkrABg0SgkACDyaolAgCE8AZWorqHXgAAAABJRU5ErkJggg==" class="fm-editor-equation" data-mlang="latex" data-equation="2"> to show that <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAcAAAAJBAMAAAAMdiuQAAAACXBIWXMAAABkAAAAZAAPlsXdAAAAKlBMVEUAAAAAAABHcEwAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACqYB4GAAAADnRSTlMziABEEaqZd2bVVSK77llg+YgAAAA1SURBVAjXY3BPUAhgaEpWF2BwmaRqwKAhpKvAoCjEo8CgnByowKDgHaDAYKmcpMDgsVxJAQC7uggmlJFTrgAAAABJRU5ErkJggg==" class="fm-editor-equation" data-mlang="latex" data-equation="y"> satisfy the equation<img src="data:image/png;base64,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" class="fm-editor-equation" data-mlang="latex" data-equation="8y%5E%7B3%7D-6y-1%3D0">

MATH 140 Lecture : derivatives - 3

MATH 140 Full Course Notes

Get access

Related textbook solutions

Calculus

Single Variable Calculus: Early Transcendentals

CALCULUS:EARLY TRANSCENDENTALS

Related Documents

MATH 140 Lecture 26: Nov 7-9

MATH 140 Lecture Notes - Lecture 5: Cube Root, Foreign Exchange Market, Farad

MATH 140 Midterm: MATH 140 Midterm 1 Summer

Related Questions